A142719 a(n) = if n < 41 then n^2 - n + 41, otherwise n^2 - 81*n + 1681.

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, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197

Offset: 1

Author

Roger L. Bagula, Sep 27 2008

Keywords

• nonn

Comments

A variation on Euler's prime generating polynomial found in a novel by Arthur C. Clarke and Gentry Lee. Gives 96 primes in first 100 terms.

Note that in n^2-81*n+1681, substitution of n= m+41 gives m^2+m+41, Euler's polynomial. So we get the same set of 40 primes twice.

References

• Arthur C. Clarke and Gentry Lee, The Garden of Rama, Dell Publishing, 1991, ISBN 0-533-29817-8, page 59.

Links

• James Clewett and Brady Haran, 41 and more Ulam's Spiral, Numberphile video, 2013.

Crossrefs

Cf. A005846.

Programs

Mathematica

f[n_]=If[n<41,n^2-n+41,n^2-81*n+1681]; Table[f[n],{n,0,100}]

Formula

a(n)=If[n < 41, n^2 - n + 41, n^2 - 81*n + 1681].

Extensions

Edited by N. J. A. Sloane, Sep 27 2008