

A178639


Numbers n such that all three values n^2+13^k, k = 1, 2, 3, are prime.


0



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

1,1


COMMENTS

Subsequence of A176969.
The leastsignificant 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.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..39.


EXAMPLE

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.


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 31 2010


EXTENSIONS

keyword:base removed by R. J. Mathar, Jul 13 2010


STATUS

approved



