A090101 Numbers n such that n and the 6 successive integers yield primes if substituted for x in polynomial 5x^2+5x+1.

1, 321, 63879, 6265151, 6921510, 9239188, 23156113, 26854544, 35917576, 45591317, 51307313, 52260254, 53855078, 71731838, 118305552, 124220571, 124234464, 150767861, 170448863, 192850264

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Example

a[15]=118305552 and the corresponding seven "polynomially consecutive" primes are: {69981018761651281, 69981019944706811, 69981021127762351, 69981022310817901, 69981023493873461, 69981024676929031, 69981025859984611}

Mathematica

po[x_] := 5*x^2+5*x+1 Do[s=po[n]; s0=po[n]; s1=po[n+1]; s2=po[n+2]; s3=po[n+3]; s4=po[n+4]; s5=po[n+5]; s6=po[n+6]; If[IntegerQ[n/100000], Print[{n}]]; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3]&&PrimeQ[s4]&&PrimeQ[s5] &&PrimeQ[s6], Print[{n, s0, s1, s2, s3, s4, s5, s6}]], {n, 1, 120000000}]
Select[Range[193*10^6], AllTrue[Table[5x^2+5x+1, {x, Range[#, #+6]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 02 2020 *)

Crossrefs

Cf. A090562, A090563, A090100, A090102.

Sequence in context: A004927 A074350 A144124 * A105952 A062205 A054034

Adjacent sequences: A090098 A090099 A090100 * A090102 A090103 A090104

Keyword

nonn

Author

Labos Elemer, Dec 12 2003

Extensions

More terms from Don Reble, Dec 14 2003

Status

approved