A196230 Euler primes: values of x^2 - x + k for x = 1..k-1, where k is one of Euler's "lucky" numbers 2, 3, 5, 11, 17, 41.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 97, 101, 107, 113, 127, 131, 149, 151, 173, 197, 199, 223, 227, 251, 257, 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

Offset

1,1

Comments

See A198245 for another sequence of "Euler primes". - N. J. A. Sloane, May 29 2022

All terms are prime numbers.

k is an Euler "lucky" number iff 4k-1 is a Heegner number 1, 2, 3, 7, 11, 19, 43, 67, 163.

See A014556 (Euler's "lucky" numbers) and A003173 (Heegner numbers) for additional references and links.

References

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 225.

Links

Table of n, a(n) for n=1..63.

Example

The prime 1601 is a member because 40^2-40+41 = 1601.

Mathematica

H = {2, 3, 5, 11, 17, 41}; Union[Flatten[Table[ Array[ #^2 - # + H[[k]] &, H[[k]] - 1], {k, 1, 6}]]]

Crossrefs

Cf. A003173, A014556, A198245.

Sequence in context: A038616 A228296 A176165 * A233360 A234960 A118850

Adjacent sequences: A196227 A196228 A196229 * A196231 A196232 A196233

Keyword

nonn,fini,full

Author

Jonathan Sondow, Oct 29 2011

Status

approved