

A057247


a(n) is the smallest prime of the form 1 + prime(n)*2^m.


1



5, 7, 11, 29, 23, 53, 137, 1217, 47, 59, 7937, 149, 83, 173
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OFFSET

1,1


COMMENTS

The prime a(15) has 449 decimal digits (see A058887).


LINKS

Table of n, a(n) for n=1..14.
JeanFrançois Alcover, Table of n, a(n) for n=16..50.


FORMULA

a(n) = Min{qq is prime, p(n) is the nth prime and q = 1+p(n)*2^b(n)}.


EXAMPLE

SophieGermain 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.


MATHEMATICA

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, (p1)/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}] (* JeanFrançois Alcover, Nov 08 2016 *)


CROSSREFS

Cf. A058887, A005384, A005385.
Sequence in context: A036491 A036490 A106330 * A157437 A213677 A330775
Adjacent sequences: A057244 A057245 A057246 * A057248 A057249 A057250


KEYWORD

nonn


AUTHOR

Labos Elemer, Jan 10 2001


STATUS

approved



