

A090111


Values of n such that P[n]=4n^2154n+1523 is prime and also {P[n+1],...,P[n+71]} are prime numbers. Namely: the terms are arguments providing a sequence of 7 polynomially consecutive primes with respect to 4x^2154x+1523 polynomial communicated by Rivera (2003).


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 45, 53, 66, 67, 84, 129, 130, 131, 266, 328, 329, 1619, 1620, 2655, 2937, 7509, 7510, 18030, 29283, 29714, 29715, 37630, 42037, 44473, 45905
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OFFSET

1,2


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..200


EXAMPLE

n=1 provides {1373, 1231, 1097, 971, 853, 743, 641} 7chain of primes.


MATHEMATICA

po[x_] := 4*x^2154*x+1523; Do[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[PrimeQ[s0]&&PrimeQ[s1] &&PrimeQ[s2]&&PrimeQ[s3]&&PrimeQ[s4]&&PrimeQ[s5]&&PrimeQ[s6], Print[n]], {n, 1, 1000000}]
Flatten[Position[Partition[Table[If[PrimeQ[4n^2154n+1523], 1, 0], {n, 46000}], 7, 1], {1, 1, 1, 1, 1, 1, 1}]] (* Harvey P. Dale, Mar 06 2015 *)


CROSSREFS

Cf. A090101, A090102, A090107A090109, A055561, A090563, A090110.
Sequence in context: A291168 A146296 A071670 * A071669 A114086 A257333
Adjacent sequences: A090108 A090109 A090110 * A090112 A090113 A090114


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 30 2003


STATUS

approved



