A342475 Prime numbers whose binary expansion contains only prime powers of 2 and the zeroth power.

5, 13, 37, 41, 137, 173, 2053, 2081, 2089, 2213, 2221, 8233, 8237, 8329, 8353, 10253, 10273, 10369, 131113, 131213, 133121, 133153, 133157, 133253, 133261, 139273, 139297, 139301, 139309, 139393, 139397, 139429, 141353, 141481, 524429, 524453, 526373, 526381, 526501

Offset

1,1

Comments

The numbers m = 2^e(0) + 2^e(1) + 2^e(2) + ... where all e(i) are either 0 or prime are 1, 4, 5, 8, 9, 12, 13, 32, 33, 36, 37, 40, 41, 44, 45, 128, 129, 132, 133, 136, 137, 140, 141, 160, 161, 164, ... The sequence contains the m which are primes. - R. J. Mathar, Apr 21 2021

Links

Table of n, a(n) for n=1..39.

Example

5 = 2^2 + 2^0 is a term.
7 = 2^2 + 2^1 + 2^0 is not a term, because the exponent 1 is not a prime.
11 = 2^3 + 2^1 + 2^0 is not a term, because the exponent 1 is not a prime.
13 = 2^3 + 2^2 + 2^0 is a term.

Mathematica

Select[Array[1 + Total@ MapIndexed[#1*2^Prime[#2] & @@ {#1, First[#2]} &, Reverse@ IntegerDigits[#, 2]] &, 140], PrimeQ] (* Michael De Vlieger, Mar 13 2021 *)

Prog

(PARI) isok(p) = if (isprime(p), my(b=Vecrev(binary(p))); sum(i=1, #b, b[i]*((i!=1) && !isprime(i-1))) == 0); \\ Michel Marcus, Apr 22 2021

Crossrefs

Cf. A004676, A326782, A342481.

Sequence in context: A333284 A141408 A238460 * A107144 A137815 A089523

Adjacent sequences: A342472 A342473 A342474 * A342476 A342477 A342478

Keyword

nonn,base

Author

Vassilis Papadimitriou, Mar 13 2021

Status

approved