OFFSET
2,9
COMMENTS
Conjecture: a(n) > 0 for every n > 1.
Records: 1, 4, 16, 37, 120, 239, 260, 472, 917, 1539, 6633, 7050, 12818, ..., which occur at n = 2, 10, 13, 17, 20, 32, 41, 52, 72, 128, 171, 290, 309, ... - Robert G. Wilson v, Jun 16 2018
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 2..345
Richard Fischer, Primzahlen mit der Form [(B+1)^N+B^N]/(2*B+1)
Henri Lifchitz & Renaud Lifchitz, Search for: (a^n+b^n)/c
EXAMPLE
a(10) = 4 because (5^29 + 4^29)/9 = 2149818248341 is prime and (2^29 + 1^29)/3, (3^29 + 2^29)/5 and (4^29 + 3^29)/7 are all composite.
MATHEMATICA
Table[p = Prime[n]; k = 1; While[q = ((b+1)^n+b^n)/(2*b+1); ! PrimeQ[q], k++]; k, {n, 200}]
f[n_] := Block[{b = 1, p = Prime@ n}, While[! PrimeQ[((b +1)^p + b^p)/(2b +1)], b++]; b]; Array[f, 70, 2] (* Robert G. Wilson v, Jun 13 2018 *)
PROG
(PARI) for(n=2, 200, b=0; until(isprime((((b+1)^prime(n)+b^prime(n))/(2*b+1))), b++); print1(b, ", ")) \\ corrected by Eric Chen, Jun 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Tim Johannes Ohrtmann, Mar 22 2018
STATUS
approved