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

Author

Jeffrey Shallit, Jun 20 2019

Keywords

• nonn
• base
• more

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

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

Crossrefs

Cf. A086342, A278966.

Formula

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