

A173854


Smallest positive integer k such that 2^n + k^2 is a prime number.


1



1, 1, 1, 3, 1, 3, 3, 3, 1, 3, 3, 9, 9, 9, 7, 15, 1, 15, 3, 9, 5, 21, 5, 3, 11, 57, 7, 21, 9, 33, 3, 27, 9, 15, 5, 39, 25, 3, 35, 57, 25, 9, 15, 33, 39, 99, 27, 3, 25, 63, 67, 9, 105, 51, 145, 33, 9, 3, 15, 57, 15, 243, 13, 111, 9, 15, 3, 81, 71, 21, 5, 21, 19, 33, 57, 81, 141, 51, 17, 33, 125
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OFFSET

0,4


COMMENTS

The list of associated primes 2^n + k^2 is 2, 3, 5, 17, 17, 41, 73, 137, 257, 521, 1033, ...
All terms are odd.  Harvey P. Dale, Dec 19 2014


REFERENCES

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
Louis J. Mordell: Diophantine equations, Academic Press Inc., 1969
Wolfgang M. Schmidt, Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics vol. 785, SpringerVerlag, 2000


LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000


EXAMPLE

2^0 + 1^2 = 2 = A000040(1) => a(0) = k = 1
2^1 + 1^2 = 3 = A000040(2) => a(1) = k = 1
2^2 + 1^2 = 5 = A000040(3) => a(2) = k = 1
2^3 + 3^2 = 17 = A000040(7) => a(3) = k = 3
2^61 + 243^2 = A000040(tbd) => a(61) = k = 243.


MAPLE

A173854 := proc(n) local twon, k ; twon := 2^n ; for k from 1 do if isprime(twon+k^2) then return k ; end if; end do ; end proc:
seq(A173854(n), n=0..90) ; # R. J. Mathar, Mar 05 2010


MATHEMATICA

spi[n_]:=Module[{t=2^n, k=1}, While[!PrimeQ[t+k^2], k=k+2]; k]; Array[spi, 90, 0] (* Harvey P. Dale, Dec 19 2014 *)


CROSSREFS

Cf. A013597, A014210.
Sequence in context: A132680 A105595 A072219 * A059789 A275367 A023136
Adjacent sequences: A173851 A173852 A173853 * A173855 A173856 A173857


KEYWORD

nonn


AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Feb 26 2010


EXTENSIONS

Extended by R. J. Mathar, Mar 05 2010


STATUS

approved



