cp's OEIS Frontend

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.

%I A332079 #15 Dec 23 2024 14:53:46
%S A332079 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,
%T A332079 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,
%U A332079 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
%N 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.
%C A332079 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.
%H A332079 T. Ordowski, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2020-August/020922.html">Problem</a>, post to the SeqFan list, Aug 11 2020.
%t A332079 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 *)
%o A332079 (PARI) apply( {A332079(n,c=0)=forprime(p=2^n,,is_A332075(p)&&return(c);c++)}, [1..99])
%Y A332079 Cf. A332075, A000040 (primes), A000265 (odd part), A007814 (2-valuation).
%K A332079 nonn
%O A332079 1,12
%A A332079 _M. F. Hasler_, Aug 13 2020