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URL: https://oeis.org/A212876

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A212876
Numbers of the form n^2+1 such that 3^(m+3)==9 (mod m) where m=n^4-1.
1
5, 17, 37, 101, 257, 1297, 4357, 14401, 44101, 65537, 828101, 933157, 8122501, 8386817, 12362257, 41990401, 121220101, 157402117, 223502501, 318622501, 378146917, 506700101, 684345601, 702038017
OFFSET
1,1
COMMENTS
All the known values of the sequence are prime (for a(n)<10^20). - Charles R Greathouse IV, Jun 07 2012
The values of n+1 are prime or composite 121, 11011, 108781, 170431...
All composite n+1 == 1 (mod 3) ???
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..3556
EXAMPLE
Let n = 10. Then m = n^4-1 = 9999. 3^10002 == 9 (mod 9999), so n^2+1 = 101 is a member of the sequence.
PROG
(PARI) v=List(); for(n=2, 1e6, m=n^4-1; if(Mod(3, m)^(m+3)==9, listput(v, n^2+1))); Vec(v) \\ Charles R Greathouse IV, May 29 2012
CROSSREFS
Sequence in context: A168024 A121326 A347300 * A147219 A146280 A282511
KEYWORD
nonn
AUTHOR
Alzhekeyev Ascar M, May 29 2012
STATUS
approved