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A155884 a(n)=n^2-n+41 if this is prime, a(n)=a(n-40) otherwise. 1
41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601, 41, 43, 1847, 1933, 61, 2111, 2203, 2297, 2393, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A variant of A005846, A060566, A142719. All these aim at extending the series of prime values of Euler's famous prime-producing polynomial P(n)=n^2+n+41 (see references in A005846).

The present sequence is a simplification of an extended variant of A142719. By construction, all terms of the present sequence are prime, but in contrast to A005846, prime values of the polynomial remain at the "correct" position (a(n)=P(n)). The "substituted" values are easily recognized as they follow local maxima. Of course one could equally well insert a(n)=2 whenever P(n) is composite.

Note that the present sequence contains only primes. A different sequence, defined by "a(n)=f(n) if this is prime, a(n)=f(n-40) otherwise, where f(n)=n^2-n+41", does not always produce primes.

LINKS

Table of n, a(n) for n=1..50.

PROG

(PARI) a(n) = { while( !isprime( n^2-n+41 ), n-=40 ); n^2-n+41 }

CROSSREFS

Cf. A005846, A060566, A142719.

Sequence in context: A282319 A257362 A296921 * A202018 A005846 A273756

Adjacent sequences:  A155881 A155882 A155883 * A155885 A155886 A155887

KEYWORD

easy,nonn

AUTHOR

Roger L. Bagula and M. F. Hasler, Jan 29 2009

STATUS

approved

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Last modified February 23 12:35 EST 2019. Contains 320431 sequences. (Running on oeis4.)