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

1,2

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

Table of n, a(n) for n=1..66.

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

Mathematica

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

Prog

(PARI) select( {is_A332076(n)=ispseudoprime((n>>n=valuation(n, 2))+2<<n)}, [1..199])

Crossrefs

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

Sequence in context: A007494 A258575 A052490 * A248562 A117672 A194383

Adjacent sequences: A332073 A332074 A332075 * A332077 A332078 A332079

Keyword

nonn

Author

M. F. Hasler, Aug 13 2020

Status

approved