A326782 Numbers whose binary indices are prime numbers.

0, 2, 4, 6, 16, 18, 20, 22, 64, 66, 68, 70, 80, 82, 84, 86, 1024, 1026, 1028, 1030, 1040, 1042, 1044, 1046, 1088, 1090, 1092, 1094, 1104, 1106, 1108, 1110, 4096, 4098, 4100, 4102, 4112, 4114, 4116, 4118, 4160, 4162, 4164, 4166, 4176, 4178, 4180, 4182, 5120

Offset: 1

Author

Gus Wiseman, Jul 25 2019

Keywords

• nonn

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

Write n = 2^e_1 + 2^e_2 + 2^e_3 + ..., with e_1>e_2>e_3>... We require that all the numbers e_i + 1 are primes. So 6 = 2^2+2^1 is OK because 2+1 and 1+1 are primes. 0 is OK because there are no e_i. - N. J. A. Sloane, Jul 27 2019

Examples

			The sequence of terms together with their binary indices begins:
     0: {}
     2: {2}
     4: {3}
     6: {2,3}
    16: {5}
    18: {2,5}
    20: {3,5}
    22: {2,3,5}
    64: {7}
    66: {2,7}
    68: {3,7}
    70: {2,3,7}
    80: {5,7}
    82: {2,5,7}
    84: {3,5,7}
    86: {2,3,5,7}
  1024: {11}
  1026: {2,11}
  1028: {3,11}
  1030: {2,3,11}
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A029931, A048793, A070939, A326031, A326701, A326781, A326788.

Programs

Maple

f:= proc(n) local L,i;
  L:= convert(n,base,2);
  add(L[i]*2^(ithprime(i)-1),i=1..nops(L))
end proc:
map(f, [$0..100]); # Robert Israel, Jul 26 2019

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
Select[Range[0,100],And@@PrimeQ/@bpe[#]&]