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A143539 Number of ways to express 2n-1 as p+2a^2; p prime, a > 0. 5
0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 3, 1, 3, 1, 1, 3, 1, 2, 3, 3, 1, 2, 3, 1, 4, 2, 1, 5, 1, 1, 5, 3, 1, 2, 4, 1, 3, 4, 2, 5, 3, 1, 4, 2, 2, 6, 2, 1, 3, 2, 3, 5, 4, 1, 5, 5, 1, 6, 3, 2, 5, 1, 2, 2, 4, 3, 5, 4, 0, 7, 4, 1, 6, 3, 1, 5, 2, 2, 5, 6, 1, 2, 5, 2, 7, 4, 2, 6, 2, 2, 9, 2, 3, 4, 4, 2, 2, 4, 1, 9, 5, 3, 5, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Similar to A046921 and A046923. Sequence A060003 lists the odd numbers having no representations.

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.

EXAMPLE

a(11)=3 because 21 = 19+2*1^2 = 13+2*2^2 = 3+2*3^2.

MATHEMATICA

Table[cnt=0; Do[If[PrimeQ[n-2*k^2], cnt++ ], {k, Floor[Sqrt[n/2]]}]; cnt, {n, 1, 20000, 2}]

CROSSREFS

Sequence in context: A195910 A240590 A080769 * A249063 A099307 A256750

Adjacent sequences:  A143536 A143537 A143538 * A143540 A143541 A143542

KEYWORD

nonn

AUTHOR

T. D. Noe, Aug 23 2008

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)