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A275530
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Smallest positive integer m such that (m^(2^n) + 1)/2 is prime.
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2
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3, 3, 3, 9, 3, 3, 3, 113, 331, 513, 827, 799, 3291, 5041, 71, 220221, 23891, 11559, 187503, 35963
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listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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The terms of this sequence with n > 11 correspond to probable primes which are too large to be proven prime currently. - Serge Batalov, Apr 01 2018
a(15) is a statistically significant outlier; the sequence (m^(2^15)+1)/2 may require a double-check with software that is not GWNUM-based. - Serge Batalov, Apr 01 2018
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LINKS
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Table of n, a(n) for n=0..19.
Richard Fischer, Generalized Fermat numbers with odd base
Wikipedia, Fermat number
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EXAMPLE
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a(7) = 113 since 113 is the smallest positive integer m such that (m^(2^7)+1)/2 is prime.
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MAPLE
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a:= proc(n) option remember; local m; for m by 2
while not isprime((m^(2^n)+1)/2) do od; m
end:
seq(a(n), n=0..8);
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MATHEMATICA
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Table[m = 1; While[! PrimeQ[(m^(2^n) + 1)/2], m++]; m, {n, 0, 9}] (* Michael De Vlieger, Sep 23 2016 *)
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PROG
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(PARI) a(n) = {my(m = 1); while (! isprime((m^(2^n)+1)/2), m += 2); m; } \\ Michel Marcus, Aug 01 2016
(Python)
from sympy import isprime
def a(n):
m, pow2 = 1, 2**n
while True:
if isprime((m**pow2 + 1)//2): return m
m += 2
print([a(n) for n in range(9)]) # Michael S. Branicky, Mar 03 2021
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CROSSREFS
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Cf. A056993, A027862.
Sequence in context: A226509 A329694 A183389 * A180637 A201539 A223747
Adjacent sequences: A275527 A275528 A275529 * A275531 A275532 A275533
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KEYWORD
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nonn,more
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AUTHOR
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Walter Kehowski, Jul 31 2016
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EXTENSIONS
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a(13)-a(14) from Robert Price, Sep 23 2016
a(15) from Serge Batalov, Mar 29 2018
a(16) from Serge Batalov, Mar 30 2018
a(17) from Serge Batalov, Apr 01 2018
a(18)-a(19) from Ryan Propper, Aug 16 2022. These correspond to 1382288- and 2388581-digit PRPs, respectively, found using an exhaustive search with Jean Penne's LLR2.
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STATUS
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approved
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