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%I #9 Jan 29 2024 19:13:04
%S 10,12,200,268,340,418,488,530,838,840,1102,1720,1830,2240,2410,2768,
%T 3148,3202,3318,3322,3958,4162,4610,5080,5672,5700,5722,5870,6178,
%U 6302,6480,7490,8130,8262,8888,9132,9602,9618,10638
%N Numbers m such that all three values m^2 + 13^k, k = 1, 2, 3, are prime.
%C Subsequence of A176969.
%C The least-significant digit of all terms is one of 0, 2 or 8, because for odd digits m^2 + 13^k would be even (not prime), and for digits 4 and 6 the number m^2 + 13^2 is a multiple of 5.
%D B. Bunch: The Kingdom of Infinite Number: A Field Guide, W. H. Freeman, 2001.
%D R. Courant, H. Robbins: What Is Mathematics? An Elementary Approach to Ideas and Methods, Oxford University Press, 1996.
%D G. H. Hardy, E. M. Wright, E. M., An Introduction to the Theory of Numbers (5th edition), Oxford University Press, 1980.
%e m=10 is in the sequence because 10^2 + 13 = 113 = prime(30), 10^2 + 13^2 = 269 = prime(57), 10^2 + 13^3 = 2297 = prime(342).
%e m=8888 is in the sequence because 8888^2 + 13 = 78996557 = prime(4614261), 8888^2 + 13^2 = 78996713 = prime(4614269), 8888^2 + 13^3 = 78998741 = prime(4614379).
%e m=6480 yields a prime 6480^2 + 13^k even for k=0.
%e m=7490 yields a prime 7490^2 + 13^k even for k=0 and k=4.
%Y Cf. A000040, A000290, A055394, A056899, A086380, A113536, A176371, A176969.
%K nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 31 2010
%E keyword:base removed by _R. J. Mathar_, Jul 13 2010
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