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A057247 a(n) is the smallest prime of the form 1 + prime(n)*2^m, with m > 0.

%I A057247 #27 May 27 2022 21:11:05
%S A057247 5,7,11,29,23,53,137,1217,47,59,7937,149,83,173
%N A057247 a(n) is the smallest prime of the form 1 + prime(n)*2^m, with m > 0.
%C A057247 The prime a(15) has 178 decimal digits. [Corrected by _Sean A. Irvine_, May 27 2022]
%H A057247 Alois P. Heinz, <a href="/A057247/b057247.txt">Table of n, a(n) for n = 1..75</a>
%H A057247 Jean-François Alcover, <a href="/A057247/a057247.txt">Table of n, a(n) for n=16..50.</a>
%F A057247 a(n) = Min{q|q is prime, p(n) is the n-th prime and q = 1+p(n)*2^b(n)}.
%e A057247 Sophie-Germain primes are here at n = 1, 2, 3, 5, 9, 10, .. etc. At n = 11, p(11) = 31 and in the sequence of q = 1+31*{2, 4, 8, 16, 32, 64, 128, 256} = {63, 125, 249, 497, 993, 1985, 3969, 7937}, the first prime is 7937, so b(11) = 8, a(11) = 7937.
%p A057247 a:= proc(n) option remember; local p, m, t; p:= ithprime(n);
%p A057247       for m do t:= 1+p*2^m; if isprime(t) then return t fi od
%p A057247     end:
%p A057247 seq(a(n), n=1..15);  # _Alois P. Heinz_, May 27 2022
%t A057247 a[n_] := (For[pn = Prime[n]; p = 2, p < 3*10^8 (* large enough to compute 50 terms except a(15) *), p = NextPrime[p], m = Log[2, (p-1)/pn]; If[m > 0 && IntegerQ[m], Print["a(", n, ") = ", p]; Return[p]]]; Print["a(", n, ") not found ", p]; 0); Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Nov 08 2016 *)
%o A057247 (Python)
%o A057247 from sympy import isprime, prime
%o A057247 def a(n):
%o A057247     m, pn = 1, prime(n)
%o A057247     while not isprime(1 + pn*2**m): m += 1
%o A057247     return 1 + pn*2**m
%o A057247 print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, May 27 2022
%Y A057247 Cf. A058887, A005384, A005385, A057192.
%K A057247 nonn
%O A057247 1,1
%A A057247 _Labos Elemer_, Jan 10 2001
%E A057247 Title clarified by _Sean A. Irvine_, May 27 2022