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A230546 Least positive integer k <= n such that 2*k^2-1 is a prime and n - k is a square, or 0 if such an integer k does not exist. 1
0, 2, 2, 3, 4, 2, 3, 4, 8, 6, 2, 3, 4, 10, 6, 7, 8, 2, 3, 4, 17, 6, 7, 8, 21, 10, 2, 3, 4, 21, 6, 7, 8, 18, 10, 11, 21, 2, 3, 4, 25, 6, 7, 8, 36, 10, 11, 39, 13, 25, 2, 3, 4, 18, 6, 7, 8, 22, 10, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

By the conjecture in A230494, we should have a(n) > 0 for all n > 1.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 3 since neither 4 - 1 = 3 nor 4 - 2 = 2 is a square, but 4 - 3 = 1 is a square and 2*3^2 - 1 = 17 is a prime.

MATHEMATICA

SQ[n_]:=IntegerQ[Sqrt[n]]

Do[Do[If[PrimeQ[2k^2-1]&&SQ[n-k], Print[n, " ", k]; Goto[aa]], {k, 1, n}];

Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 60}]

CROSSREFS

Cf. A000040, A000290, A066049, A230351, A230362, A230493, A230494.

Sequence in context: A236241 A127731 A159978 * A286617 A328446 A257062

Adjacent sequences:  A230543 A230544 A230545 * A230547 A230548 A230549

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Oct 23 2013

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)