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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.
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%I #13 May 29 2022 15:49:30

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,83,89,97,

%T 101,107,113,127,131,149,151,173,197,199,223,227,251,257,281,313,347,

%U 383,421,461,503,547,593,641,691,743,797,853,911,971,1033,1097,1163,1231,1301,1373,1447,1523,1601

%N 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.

%C See A198245 for another sequence of "Euler primes". - _N. J. A. Sloane_, May 29 2022

%C All terms are prime numbers.

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

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

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

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

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

%Y Cf. A003173, A014556, A198245.

%K nonn,fini,full

%O 1,1

%A _Jonathan Sondow_, Oct 29 2011