A214518 - OEIS

A214518

Record differences between the numbers n such that 4*n^2 + 1 is prime.

1, 2, 5, 7, 8, 10, 17, 20, 23, 44, 50, 56, 65, 76, 106, 144, 165, 173

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OFFSET

1,2

LINKS

EXAMPLE

a(1) = 1 because 4*1^2 + 1 = 5 and 4*2^2 + 1 = 17 are primes.

a(2) = 2 because 4*3^2 + 1 = 37 is prime, 4*4^2 + 1 = 65 is composite, and 4*5^2 + 1 = 101 is prime.

a(3) = 5 because 4*13^2 + 1 is prime, 4*n^2 + 1 is composite for n = 14..17, and 4*18^2 + 1 is prime.

MATHEMATICA

n = 1; last = 1; t = {1}; While[Length[t] < 15, n++; p = 1 + 4*n^2; If[PrimeQ[p], If[n - last > t[[-1]], AppendTo[t, n - last]]; last = n]]; t

CROSSREFS

Cf. A121326 (primes of the form 1+4*n^2), A001912 (values of n).

Cf. A214517 (differences), A214519 (where record differences occur).

KEYWORD

nonn,hard,more

AUTHOR

T. D. Noe, Aug 06 2012

STATUS

approved