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A238554
Smallest k such that k + 2^n and k*2^n + 1 are both prime.
4
1, 1, 1, 5, 1, 11, 3, 9, 1, 35, 15, 39, 3, 39, 63, 35, 1, 149, 3, 419, 7, 221, 25, 155, 73, 735, 69, 29, 193, 261, 3, 135, 81, 149, 85, 125, 117, 809, 303, 509, 27, 699, 325, 29, 27, 285, 639, 65, 61, 1911, 639, 165, 295, 1295, 163, 905, 175, 75, 1593, 249
OFFSET
0,4
COMMENTS
If a(n) = 1, then the two primes are the same and they are Fermat primes. - Michel Marcus, Mar 01 2014
LINKS
EXAMPLE
5 is in this sequence because 5 + 2^3 = 13 and 5*2^3 + 1 = 41 are both prime.
MATHEMATICA
Table[Module[{k=1, c=2^n}, While[!AllTrue[{c+k, k c+1}, PrimeQ], k++]; k], {n, 0, 60}] (* Harvey P. Dale, Oct 20 2023 *)
PROG
(PARI) a(n) = {k = 1; while (!(isprime(k + 2^n) && isprime(k*2^n + 1)), k++); k; } \\ Michel Marcus, Mar 01 2014
CROSSREFS
Cf. A019434 (Fermat primes).
Sequence in context: A347389 A330774 A296307 * A067292 A131782 A242060
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(15) corrected and a(24) from Michel Marcus, Mar 01 2014
Missing term and a(25)-a(59) from Giovanni Resta, Mar 01 2014
STATUS
approved