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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 (list; graph; refs; listen; history; text; internal format)
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, Springer-Verlag, 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

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Last modified February 18 12:10 EST 2020. Contains 332018 sequences. (Running on oeis4.)