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

1,2

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

Links

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

Example

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}

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[#]&]

Crossrefs

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

Sequence in context: A037019 A369099 A341668 * A358126 A096174 A096173

Adjacent sequences: A326779 A326780 A326781 * A326783 A326784 A326785

Keyword

nonn

Author

Gus Wiseman, Jul 25 2019

Status

approved