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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.
3
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 13 2020
STATUS
approved