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A142719
a(n) = if n < 41 then n^2 - n + 41, otherwise n^2 - 81*n + 1681.
3
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
1,1
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.
FORMULA
a(n)=If[n < 41, n^2 - n + 41, n^2 - 81*n + 1681].
MATHEMATICA
f[n_]=If[n<41, n^2-n+41, n^2-81*n+1681]; Table[f[n], {n, 0, 100}]
CROSSREFS
Cf. A005846.
Sequence in context: A155769 A247390 A291501 * A155884 A284043 A191754
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 27 2008
EXTENSIONS
Edited by N. J. A. Sloane, Sep 27 2008
STATUS
approved