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A326782
Numbers whose binary indices are prime numbers.
18
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
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[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved