Vincenzo Manto is the author of 14 sequences in the OEIS. His work has contributed significantly to the field of integer sequences, ranging from "Numbers whose number of nonzero digits is identical in base 2 and 3." to "Primes prime(k) such that prime(k) - prime(k-1) is a Fibonacci number.".
His most prolific partners include James C. McMahon.
His contributions have been cited in 16 other sequences, showcasing the impact of his work on the OEIS community, making him a 88-percentile contributor
Numbers whose number of nonzero digits is identical in base 2 and 3.
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Smallest number k > n such that the binary Hamming distance between n and k is equal to the number of runs in the binary representation of n, and k has more runs than n.
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a(n) is the integer obtained by inserting the sum (modulo 10) of adjacent digits of n between them.
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Numbers k such that k is coprime to each of its digits and to the sum of its digits.
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Maximum number of runs in the binary expansion of integers obtained by changing a single 0-bit to 1 in the binary representation of n considering bits up to and including the first leading 0.
- The bit-flip is allowed on any 0-bit within the standard binary representation of n, or on the first implicit leading zero (at position floor(log_2(n)) + 1). This identifies the maximum disruption to the run-length encoding (A005811) caused by a single-bit increment at Hamming distance 1. Therefore, this sequence provides a measure of how a single-bit change at Hamming distance 1 can disrupt the compression efficiency (RLE) of the binary representation of n.
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Numbers whose number of nonzero digits is identical in base 2 and 5.
- Numbers k such that A000120(k) = A276134(k).
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a(n) is the integer obtained by inserting the product (modulo 10) of adjacent digits of n between them.
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Sum of the cumulative number of previous occurrences of the digits of n in the sequence 1..n excluding the current occurrence of each digit.
- This sequence is the exclusive counterpart to A343644. While A343644 counts the occurrences of digits in the range [1,n], a(n) counts only the occurrences strictly preceding each digit of n. Formally a(n) = A343644(n) - A055642(n). Thus, this sequence represents the exclusive scan of digit occurrences, whereas A343644 is the inclusive scan. a(n) = 0 for all single-digit n as it measures the cumulative repetition of digits at the exact moment n is formed.
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Strictly increasing minimal sequence where consecutive terms can be added digit-by-digit without carrying in base 10.
- Many integers (e.g., 6, 7, 8, 9, 15, 16...) are never present because the greedy behavior and the strictly increasing condition bypass them to avoid carries.
- A subset of nonnegative integers with no decimal digits > 5 (A007092).
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Numbers such that each digit d_i is equal to the number of digits to its right that are strictly less than d_i.
- For a number with L digits d_1, d_2, ..., d_L, the rule is d_i = #{j > i : d_j < d_i}.
- The last digit d_L is always 0 because there are no digits to its right.
- The first digit d_1 is always between 1 and L-1.
- Therefore, a number of length L is in the sequence if its digits d_i (for i=0..L-1) satisfy d_0 = L-1, d_{L-1} = 0, and d_i is either 0 or L-1-i for 0 < i < L-1.
- Thus, each digit describes the 'downward slope' of the remaining digits to its right.
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Primes p such that the Fermat quotient q = (2^(p-1) - 1)/p mod p satisfies 1 < q < p and q divides p - 1.
- All known Mersenne primes (A000668) > 3 are terms of this sequence.
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Primes prime(k) such that prime(k) - prime(k-1) is a factorial.
- The sequence consists of all primes prime(k) for which the gap to the previous prime prime(k-1) is a factorial.
- Every upper member of a twin prime (A006512) pair belongs to the sequence, since 2 = 2!.
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Primes prime(k) such that prime(k) - prime(k-1) is a Fibonacci number.
- Fibonacci numbers grow exponentially while the average gap between consecutive primes grows logarithmically, thus this sequence's density decreases as k increases.
- It is conjectured that this sequence is infinite as a consequence of the Polignac's conjecture.
- Infinite if the Twin Prime conjecture holds. - _Michael S. Branicky_, May 24 2026
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