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A253633 a(n) is the least positive integer b such that b^(2^n) + (b-1)^(2^n) is prime. 4
2, 2, 2, 2, 2, 9, 96, 32, 86, 60, 1079, 755, 312, 3509, 1829, 49958, 22845 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
When a(n) is 2, the corresponding prime is a Fermat prime, otherwise it is a so-called extended generalized Fermat prime sometimes denoted xGF(n, b, b-1) or similar.
LINKS
Henri Lifchitz & Renaud Lifchitz, PRP Top Records, search for x^16384+y^16384, related to a(14).
Henri Lifchitz & Renaud Lifchitz, 49958^32768+49957^32768, a(15).
Henri Lifchitz & Renaud Lifchitz, 22845^65536+22844^65536, a(16).
FORMULA
a(n) = A080208(n) + 1.
EXAMPLE
For n = 5, 2^5 = 32 is the exponent. The numbers 1^32 + 0^32, 2^32 + 1^32, ..., 8^32 + 7^32 are not prime, but 9^32 + 8^32 is prime, so a(5) = 9. - Michael B. Porter, Mar 28 2018
PROG
(PARI) a(n)=for(b=2, 10^10, if(ispseudoprime(b^(2^n)+(b-1)^(2^n)), return(b)))
CROSSREFS
Sequence in context: A323443 A334511 A291944 * A216844 A088050 A260725
KEYWORD
nonn,hard,more
AUTHOR
Jeppe Stig Nielsen, Jan 07 2015
EXTENSIONS
a(13) from Jeppe Stig Nielsen, Mar 27 2018
a(14) found by Henri Lifchitz in 2007, from Jeppe Stig Nielsen, Apr 17 2018
a(15) found by Kellen Shenton, from Jeppe Stig Nielsen, Nov 27 2020
a(16) found by Kellen Shenton, from Jeppe Stig Nielsen, Mar 31 2021
STATUS
approved

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Last modified February 24 14:43 EST 2024. Contains 370305 sequences. (Running on oeis4.)