A332076 Indices n of odd numbers 2n+1 such that k + 2^m is prime, where k and m are the odd part and 2-valuation, respectively, of 2n.

1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 24, 26, 27, 29, 30, 35, 36, 38, 39, 41, 44, 45, 50, 51, 54, 56, 57, 59, 60, 65, 66, 69, 71, 74, 77, 78, 80, 81, 84, 86, 87, 92, 95, 96, 98, 99, 101, 104, 105, 107, 110, 111, 114, 116, 120, 125, 126, 128, 129, 132, 134

Offset: 1

Author

M. F. Hasler, Aug 13 2020

Keywords

• nonn

Comments

It appears that about 1/log_10(N) of the odd numbers below 2N have this property: for n < 10^k with k = (1, 2, 3, 4, 5, 6), there are (7, 51, 364, 2675, 20668, 167185) numbers as defined in NAME.

See the sequence A332075 of the corresponding odd numbers for more information.

Links

• T. Ordowski, Problem, post to the SeqFan list, Aug. 11, 2020

Crossrefs

Cf. A000040 (primes), A000265 (odd part), A007814 (2-valuation), A332075 (the corresponding odd numbers).

Programs

Mathematica

Select[Range[134], PrimeQ[(m = 2^IntegerExponent[2*#, 2]) + 2*#/m] &] (* Amiram Eldar, Aug 16 2020 *)

PARI

select( {is_A332076(n)=ispseudoprime((n>>n=valuation(n,2))+2<