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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved