A332079 Number of primes between 2^n and the least prime p > 2^n in A332075, i.e., such that k + 2^m is prime, where k and m are the odd part and 2-valuation, respectively, of p-1.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 8, 1, 9, 7, 0, 0, 7, 5, 1, 2, 4, 9, 1, 7, 8, 6, 11, 0, 4, 0, 1, 1, 0, 0, 10, 17, 3, 0, 8, 0, 10, 20, 3, 23, 15, 3, 20, 13, 7, 36, 17, 15, 4, 4, 0, 9, 15, 10, 21, 8, 22, 36, 6, 13, 2, 7, 36, 14, 10, 9, 4, 0, 44, 10, 8, 27, 5, 1, 0, 2, 22, 3, 2, 33, 20, 21, 19, 12, 12, 5

Offset

1,12

Comments

It appears that the sequence of odd numbers k*2^m+1 such that k + 2^m is prime (A332075) mainly consists of primes, and many primes are in this sequence. This sequence attempts to measure in how far this remains true for large numbers.

Links

Table of n, a(n) for n=1..91.

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

Mathematica

a[n_] := Module[{count = 0, p = NextPrime[2^n]}, While[!PrimeQ[(m = 2^IntegerExponent[p - 1, 2]) + (p - 1)/m], count++; p = NextPrime[p]]; count]; s = Array[a, 100] (* Amiram Eldar, Aug 14 2020 *)

Prog

(PARI) apply( {A332079(n, c=0)=forprime(p=2^n, , is_A332075(p)&&return(c); c++)}, [1..99])

Crossrefs

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

Sequence in context: A225667 A021126 A091557 * A196765 A182526 A298519

Adjacent sequences: A332076 A332077 A332078 * A332080 A332081 A332082

Keyword

nonn

Author

M. F. Hasler, Aug 13 2020

Status

approved