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URL: https://oeis.org/A092558

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A092558
Numbers k such that 2^k +- 1 are both semiprimes.
7
11, 23, 101, 167, 199, 347
OFFSET
1,1
COMMENTS
Intersection of A092559 and A085724.
a(7), if it exists, is at least 41519. - Charles R Greathouse IV, Jun 05 2013
2^41519 + 1 is the product of 3 and a composite number, so if a(7) exists, it exceeds 41519. - Jon E. Schoenfield, Feb 22 2022
EXAMPLE
11 is a term because 2^11 - 1 = 23*89 and 2^11 + 1 = 3*683.
MAPLE
q:= n-> andmap(x-> ifactors(x)[2][.., 2]=[1$2], [2^n-1, 2^n+1]):
select(q, [$1..200])[]; # Alois P. Heinz, Oct 17 2025
PROG
(PARI) is(n)=isprime(n) && n>7 && ispseudoprime((2^n+1)/3) && bigomega(2^n-1)==2 \\ Charles R Greathouse IV, Jun 05 2013
CROSSREFS
Subsequence of A000040.
Sequence in context: A077707 A081981 A081982 * A294255 A088777 A041238
KEYWORD
nonn
AUTHOR
Zak Seidov, Feb 27 2004
EXTENSIONS
a(6) from Robert G. Wilson v, Apr 18 2006
STATUS
approved