A308730 Smallest prime p for which n is the least number of 1's in the base-2 representation of a multiple of p.

2, 3, 7, 89, 31, 13367, 127, 2099863, 178481

Offset

1,1

Comments

It is not known if a(n) actually exists for all n. If there are infinitely many Mersenne primes, then a(n) is defined for infinitely many n.

The corresponding multipliers for n = 1,2,...,7 are 1,1,1,1,1,5,1,1,1. (Computations done by Leon Witzman.)

Links

Table of n, a(n) for n=1..9.

K. B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica 38 (1980), 117-128, DOI:10.4064/aa-38-2-117-128.

Formula

A086342(a(n)) = n. - Rémy Sigrist, Jul 06 2019

Crossrefs

Cf. A086342, A278966.

Sequence in context: A288800 A247025 A053964 * A062578 A062529 A308917

Adjacent sequences: A308727 A308728 A308729 * A308731 A308732 A308733

Keyword

nonn,base,more

Author

Jeffrey Shallit, Jun 20 2019

Status

approved