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A001912
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Numbers k such that 4*k^2 + 1 is prime.
(Formerly M0636 N0232)
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43
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1, 2, 3, 5, 7, 8, 10, 12, 13, 18, 20, 27, 28, 33, 37, 42, 45, 47, 55, 58, 60, 62, 63, 65, 67, 73, 75, 78, 80, 85, 88, 90, 92, 102, 103, 105, 112, 115, 118, 120, 125, 128, 130, 132, 135, 140, 142, 150, 153, 157, 163, 170, 175, 192, 193, 198, 200
(list;
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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Positive integers whose square is the sum of two triangular numbers in exactly one way (A000217(k) + A000217(k+1) = k*(k+1)/2 + (k+1)*(k+2)/2 = (k+1)^2). In other words, positive integers k such that A052343(k^2) = 1. - Altug Alkan, Jul 06 2016
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REFERENCES
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E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, Gordon and Breach, NY, 1971, p. 1.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 11.
C. S. Ogilvy, Tomorrow's Math. 2nd ed., Oxford Univ. Press, 1972, p. 116.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]
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FORMULA
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MAPLE
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option remember;
if n = 1 then
1;
else
for a from procname(n-1)+1 do
if isprime(4*a^2+1) then
return a;
end if;
end do:
end if;
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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