A267289 Primes p such that (2^k)+p+(2^(k+1)) is also prime, where 2^k is the largest power of 2 smaller than p.

5, 7, 13, 19, 23, 31, 41, 43, 53, 61, 71, 79, 89, 101, 137, 139, 157, 163, 173, 179, 193, 223, 229, 233, 263, 271, 281, 283, 293, 349, 383, 419, 433, 449, 461, 463, 491, 509, 547, 563, 577, 593, 601, 607, 617, 643, 677, 701, 733, 751, 757, 761, 773, 797, 811, 821, 853, 857, 863, 881, 887, 911, 937, 941, 967

Offset

1,1

Comments

Primes p such that p + 3*A053644(p) is also prime. - Robert Israel, Jan 13 2016

Links

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

Example

p = 5: 4 + 5 + 8 = 17 (is prime).
p = 7: 4 + 7 + 8 = 19 (is prime).
p = 31: 16 + 31 + 32 = 79 (is prime).
p = 43: 32 + 43 + 64 = 139 (is prime).
p = 71: 64 + 71 + 128 = 263 (is prime).
p = 89: 64 + 89 + 128 = 281 (is prime).

Maple

select(t -> isprime(t) and isprime(t + 3*2^ilog2(t)), [seq(i, i=3..10^4, 2)]); # Robert Israel, Jan 13 2016

Mathematica

Select[Prime@ Range@ 165, Function[k, PrimeQ[(2^k) + # + (2^(k + 1))]]@ Floor@ Log2@ # &] (* Michael De Vlieger, Jan 12 2016 *)
lp2Q[p_]:=Module[{k=Floor[Log[2, p]]}, PrimeQ[2^k+p+2^(k+1)]]; Select[ Prime[ Range[200]], lp2Q] (* Harvey P. Dale, Nov 02 2021 *)

Crossrefs

Sequence in context: A114275 A350429 A156107 * A084932 A038908 A314326

Adjacent sequences: A267286 A267287 A267288 * A267290 A267291 A267292

Keyword

nonn

Author

Emre APARI, Jan 12 2016

Status

approved