A353137 Primes whose gaps to both neighbor primes are powers of two.

3, 5, 7, 11, 13, 17, 19, 41, 43, 71, 97, 101, 103, 107, 109, 193, 197, 227, 229, 281, 311, 313, 349, 397, 401, 457, 461, 463, 487, 491, 499, 617, 643, 743, 761, 769, 823, 827, 857, 859, 881, 883, 911, 937, 1091, 1093, 1279, 1301, 1303, 1427, 1429, 1447, 1451

Offset: 1

Author

Alois P. Heinz, Apr 25 2022

Keywords

• nonn

Examples

			Prime 1447 is a term, the gap to the previous prime 1439 is 8 and the gap to the next prime 1451 is 4 and both gaps are powers of two.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000079, A353088, A353135, A353136.

Programs

Maple

p2:= proc(n) option remember; is(n=2^ilog2(n)) end:
q:= n-> isprime(n) and andmap(p2, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..3000])[];

Mathematica

p2[n_] := n == 2^Floor[Log2[n]];
q[n_] := PrimeQ[n] && p2[n-NextPrime[n, -1]] && p2[NextPrime[n]-n];
Select[Range[3, 3000], q] (* Jean-François Alcover, May 14 2022, after Alois P. Heinz *)