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A090100
Numbers n such that n and the four successive integers produce primes if substituted for x in the polynomial 5x^2+5x+1. See A090562, A090563. Terms show that longer similar chains also exist.
2
1, 2, 3, 13, 266, 321, 322, 323, 344, 641, 1324, 5436, 16700, 16701, 19857, 19858, 28151, 28152, 30648, 31253, 32045, 45773, 48710, 50923, 52397, 57357, 57358, 63879, 63880, 63881, 72615, 73164, 73165, 78785, 81831, 87640, 87641, 91116
OFFSET
1,2
COMMENTS
For examples of longer similar chains, if n = 1, 321, or 63879, the polynomial produces 7 consecutive prime terms (including n). - Harvey P. Dale, May 04 2024
MATHEMATICA
Do[s=5*n^2+5*n+1; s1=5*(n+1)^2+5*(n+1)+1; s2=5*(n+2)^2+5*(n+2)+1; s3=5*(n+3)^2+5*(n+3)+1; s4=5*(n+4)^2+5*(n+4)+1; If[PrimeQ[s]&&PrimeQ[s1]&&PrimeQ[s2]&& PrimeQ[s3]&&PrimeQ[s4], Print[n]], {n, 1, 100000}]
SequencePosition[Table[If[PrimeQ[5n^2+5n+1], 1, 0], {n, 100000}], {1, 1, 1, 1, 1}][[;; , 1]] (* Harvey P. Dale, May 04 2024 *)
CROSSREFS
Sequence in context: A270403 A119564 A132358 * A270314 A132484 A376060
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, Dec 12 2003
STATUS
approved