This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178639 #9 Jan 29 2024 19:13:04 %S A178639 10,12,200,268,340,418,488,530,838,840,1102,1720,1830,2240,2410,2768, %T A178639 3148,3202,3318,3322,3958,4162,4610,5080,5672,5700,5722,5870,6178, %U A178639 6302,6480,7490,8130,8262,8888,9132,9602,9618,10638 %N A178639 Numbers m such that all three values m^2 + 13^k, k = 1, 2, 3, are prime. %C A178639 Subsequence of A176969. %C A178639 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 A178639 B. Bunch: The Kingdom of Infinite Number: A Field Guide, W. H. Freeman, 2001. %D A178639 R. Courant, H. Robbins: What Is Mathematics? An Elementary Approach to Ideas and Methods, Oxford University Press, 1996. %D A178639 G. H. Hardy, E. M. Wright, E. M., An Introduction to the Theory of Numbers (5th edition), Oxford University Press, 1980. %e A178639 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 A178639 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 A178639 m=6480 yields a prime 6480^2 + 13^k even for k=0. %e A178639 m=7490 yields a prime 7490^2 + 13^k even for k=0 and k=4. %Y A178639 Cf. A000040, A000290, A055394, A056899, A086380, A113536, A176371, A176969. %K A178639 nonn %O A178639 1,1 %A A178639 Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 31 2010 %E A178639 keyword:base removed by _R. J. Mathar_, Jul 13 2010