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

Offset: 1

Author

Labos Elemer, Dec 12 2003

Keywords

• easy
• nonn

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

Crossrefs

Cf. A090562, A090563.

Programs

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 *)