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

Author

Jonathan Sondow, Oct 29 2011

Keywords

• nonn
• fini
• full

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.

Examples

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

References

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

Crossrefs

Cf. A003173, A014556, A198245.

Programs

Mathematica

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