A155884 a(n) = n^2 - n + 41 if this is a prime, a(n) = a(n-40) otherwise.

41, 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

Offset

0,1

Comments

It is well known that for 0 <= n <= 40, the polynomial f(n) = n^2 - n + 41 does yield a prime number, so the sequence is well defined.

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 considers f(n) = P(n-1) which is completely equivalent.]

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) = f(n). The "substituted" values are easily recognized as they follow local maxima. Of course one could equally well insert a(n) = 2 whenever f(n) is composite.

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", does not always produce primes.

Links

Table of n, a(n) for n=0..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: A247390 A291501 A142719 * A284043 A191754 A165862

Adjacent sequences: A155881 A155882 A155883 * A155885 A155886 A155887

Keyword

easy,nonn

Author

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

Status

approved