A371971 a(n) is the least exponent m minimizing the percentage of set bits in the binary representation of prime(n)^m.

24, 25, 12, 6, 16, 2, 10, 2, 7, 22, 16, 8, 15, 2, 14, 3, 20, 2, 4, 7, 21, 4, 19, 6, 13, 6, 7, 7, 3, 10, 2, 1, 9, 5, 2, 2, 6, 10, 36, 11, 13, 2, 2, 10, 9, 5, 2, 34, 5, 2, 4, 4, 8, 2, 9, 4, 6, 9, 3, 14, 38, 9, 14, 16, 2, 7, 4, 16, 3, 9, 6, 2, 4, 2, 10, 15, 10, 14, 6, 71, 31, 4

Offset

2,1

Links

Table of n, a(n) for n=2..83.

Hugo Pfoertner, Logfile of downward searches for {3, 5, 7, 11, 13}^m, m = 10^6 .. 1.

Hugo Pfoertner, Plot of Hammingweight(3^m)/log_2(3^m), m=2..645.

Prog

(PARI) a371971(n, limit=10000) = {my(p=prime(n), q=1, m=1); for (k=1, limit, my (pp=p^k, h=hammingweight(pp), g=#binary(pp), qq=h/g); if (qq<q, q=qq; m=k)); m};

Crossrefs

Cf. A000120, A070939, A011754, A118738, A369857.

Sequence in context: A165845 A189049 A239153 * A004513 A004465 A271232

Adjacent sequences: A371968 A371969 A371970 * A371972 A371973 A371974

Keyword

nonn,base

Author

Hugo Pfoertner, Apr 17 2024

Status

approved