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A178639
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Numbers n such that all three values n^2+13^k, k = 1, 2, 3, are prime.
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0
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10, 12, 200, 268, 340, 418, 488, 530, 838, 840, 1102, 1720, 1830, 2240, 2410, 2768, 3148, 3202, 3318, 3322, 3958, 4162, 4610, 5080, 5672, 5700, 5722, 5870, 6178, 6302, 6480, 7490, 8130, 8262, 8888, 9132, 9602, 9618, 10638
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OFFSET
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1,1
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COMMENTS
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Subsequence of A176969.
The least-significant digit of all entries is one of 0, 2 or 8, because for odd digits n^2+13^k would be even (not prime), and for digits 4 and 6 the number n^2 + 13^2 is a multiple of 5.
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REFERENCES
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B. Bunch: The Kingdom of Infinite Number: A Field Guide, W.H. Freeman, 2001
R. Courant, H. Robbins: What Is Mathematics? An Elementary Approach to Ideas and Methods, Oxford University Press, 1996
G. H. Hardy, E. M. Wright, E. M., An Introduction to the Theory of Numbers (5th edition), Oxford University Press, 1980
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LINKS
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Table of n, a(n) for n=1..39.
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EXAMPLE
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n=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).
n=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).
n=6480 defines a prime 6480^2+13^k even for k=0.
n=7490 defines a prime 7490^2+13^k even for k=0 and k=4.
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CROSSREFS
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Cf. A000040, A000290, A055394, A056899, A086380, A113536, A176371, A176969
Sequence in context: A155005 A219213 A078217 * A087392 A255534 A262422
Adjacent sequences: A178636 A178637 A178638 * A178640 A178641 A178642
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 31 2010
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EXTENSIONS
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keyword:base removed by R. J. Mathar, Jul 13 2010
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STATUS
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approved
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