A090100 - OEIS

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.

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

(list; graph; refs; listen; history; text; internal format)

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

LINKS

Table of n, a(n) for n=1..38.

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

Cf. A090562, A090563.

Sequence in context: A270403 A119564 A132358 * A270314 A132484 A376060

Adjacent sequences: A090097 A090098 A090099 * A090101 A090102 A090103

KEYWORD

easy,nonn

AUTHOR

Labos Elemer, Dec 12 2003

STATUS

approved