

A155884


a(n)=n^2n+41 if this is prime, a(n)=a(n40) 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
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OFFSET

1,1


COMMENTS

A variant of A005846, A060566, A142719. All these aim at extending the series of prime values of Euler's famous primeproducing 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(n40) otherwise, where f(n)=n^2n+41", does not always produce primes.


LINKS

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


PROG

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



