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A326782 Numbers whose binary indices are prime numbers. 2

%I

%S 0,2,4,6,16,18,20,22,64,66,68,70,80,82,84,86,1024,1026,1028,1030,1040,

%T 1042,1044,1046,1088,1090,1092,1094,1104,1106,1108,1110,4096,4098,

%U 4100,4102,4112,4114,4116,4118,4160,4162,4164,4166,4176,4178,4180,4182,5120

%N Numbers whose binary indices are prime numbers.

%C 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.

%C 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

%H Robert Israel, <a href="/A326782/b326782.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of terms together with their binary indices begins:

%e 0: {}

%e 2: {2}

%e 4: {3}

%e 6: {2,3}

%e 16: {5}

%e 18: {2,5}

%e 20: {3,5}

%e 22: {2,3,5}

%e 64: {7}

%e 66: {2,7}

%e 68: {3,7}

%e 70: {2,3,7}

%e 80: {5,7}

%e 82: {2,5,7}

%e 84: {3,5,7}

%e 86: {2,3,5,7}

%e 1024: {11}

%e 1026: {2,11}

%e 1028: {3,11}

%e 1030: {2,3,11}

%p f:= proc(n) local L,i;

%p L:= convert(n,base,2);

%p add(L[i]*2^(ithprime(i)-1),i=1..nops(L))

%p end proc:

%p map(f, [$0..100]); # _Robert Israel_, Jul 26 2019

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t Select[Range[0,100],And@@PrimeQ/@bpe[#]&]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 25 2019

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Last modified April 13 02:47 EDT 2021. Contains 342934 sequences. (Running on oeis4.)