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A057247
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a(n) is the smallest prime of the form 1 + prime(n)*2^m, with m > 0.
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1
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5, 7, 11, 29, 23, 53, 137, 1217, 47, 59, 7937, 149, 83, 173
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OFFSET
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1,1
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COMMENTS
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The prime a(15) has 178 decimal digits. [Corrected by Sean A. Irvine, May 27 2022]
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..75
Jean-François Alcover, Table of n, a(n) for n=16..50.
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FORMULA
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a(n) = Min{q|q is prime, p(n) is the n-th prime and q = 1+p(n)*2^b(n)}.
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EXAMPLE
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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.
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MAPLE
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a:= proc(n) option remember; local p, m, t; p:= ithprime(n);
for m do t:= 1+p*2^m; if isprime(t) then return t fi od
end:
seq(a(n), n=1..15); # Alois P. Heinz, May 27 2022
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MATHEMATICA
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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 *)
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PROG
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(Python)
from sympy import isprime, prime
def a(n):
m, pn = 1, prime(n)
while not isprime(1 + pn*2**m): m += 1
return 1 + pn*2**m
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, May 27 2022
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CROSSREFS
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Cf. A058887, A005384, A005385, A057192.
Sequence in context: A036491 A036490 A106330 * A157437 A213677 A330775
Adjacent sequences: A057244 A057245 A057246 * A057248 A057249 A057250
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jan 10 2001
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EXTENSIONS
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Title clarified by Sean A. Irvine, May 27 2022
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STATUS
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approved
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