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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.
1
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.
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
KEYWORD
nonn,fini,full
AUTHOR
Jonathan Sondow, Oct 29 2011
STATUS
approved