A046922 -id:A046922 - cp's OEIS frontend

A046921 Number of ways to express 2n+1 as p+2a^2; p = 1 or prime, a >= 0.

1, 2, 2, 2, 2, 2, 3, 2, 1, 4, 3, 2, 3, 1, 2, 4, 2, 2, 4, 3, 2, 3, 3, 2, 4, 3, 2, 5, 1, 2, 6, 3, 1, 3, 4, 2, 5, 4, 2, 6, 3, 2, 4, 2, 3, 6, 2, 1, 4, 3, 4, 6, 4, 2, 6, 5, 2, 6, 3, 2, 5, 1, 2, 3, 5, 4, 5, 4, 1, 8, 4, 1, 6, 3, 2, 6, 2, 2, 6, 6, 1, 4, 5, 3, 7, 4, 3, 6, 2, 3, 10, 2, 3, 4, 4, 3, 3, 4, 2

Offset: 0

David W. Wilson

nonn

Goldbach conjectured this sequence is never zero.

The only zero terms appear to be for the odd numbers 5777 and 5993. - T. D. Noe, Aug 23 2008

T. D. Noe, Table of n, a(n) for n = 0..10000
L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.
Index entries for sequences related to Goldbach conjecture

Cf. A042978, A046920, A046922, A046923, A060003, A143539.

Cf. A007697.

a046921 = a046920 . a005408  -- Reinhard Zumkeller, Apr 03 2013

a(n) = A046920(A005408(n)). - Reinhard Zumkeller, Apr 03 2013

A046923 Number of ways to express 2n+1 as p+2a^2; p prime, a >= 0.

Original entry on oeis.org

0, 1, 2, 2, 1, 2, 3, 2, 1, 3, 3, 2, 3, 1, 2, 4, 1, 2, 4, 3, 2, 3, 3, 2, 4, 2, 2, 5, 1, 2, 6, 3, 1, 3, 4, 2, 4, 4, 2, 6, 3, 2, 4, 2, 3, 6, 2, 1, 4, 2, 4, 6, 4, 2, 6, 5, 2, 6, 3, 2, 5, 1, 2, 3, 4, 4, 5, 4, 1, 8, 4, 1, 6, 3, 2, 6, 2, 2, 6, 6, 1, 3, 5, 3, 7, 4, 3, 6, 2, 3, 10, 2, 3, 4, 4, 3, 3, 4, 2

Offset: 0

David W. Wilson

nonn

The only zero terms appear to be for the odd numbers 1, 5777 and 5993. - T. D. Noe, Aug 23 2008

a(n) = A046922(A005408(n)). - Reinhard Zumkeller, Apr 03 2013

T. D. Noe, Table of n, a(n) for n = 0..10000
L. Hodges, A lesser-known Goldbach conjecture, Math. Mag., 66 (1993), 45-47.
Index entries for sequences related to Goldbach conjecture

Cf. A042978, A046920, A046921, A046922, A060003, A143539

a046923 = a046922 . a005408  -- Reinhard Zumkeller, Apr 03 2013

Definition corrected by T. D. Noe, Aug 23 2008

A046920 Number of ways to express n as p+2a^2; p = 1 or prime, a >= 0.

Original entry on oeis.org

1, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 3, 0, 2, 0, 1, 0, 4, 1, 3, 0, 2, 0, 3, 0, 1, 0, 2, 0, 4, 0, 2, 1, 2, 0, 4, 0, 3, 0, 2, 0, 3, 0, 3, 0, 2, 0, 4, 0, 3, 1, 2, 0, 5, 0, 1, 0, 2, 0, 6, 0, 3, 0, 1, 0, 3, 0, 4, 0, 2, 0, 5, 1, 4, 0, 2, 0, 6, 0, 3, 0, 2, 0, 4, 0, 2, 0, 3, 0, 6, 0, 2, 0, 1, 0, 4, 0, 3

Offset: 1

David W. Wilson

nonn

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.
Index entries for sequences related to Goldbach conjecture

Cf. A042978, A046921, A046922, A046923, A060003, A143539.

Cf. A016067, A008578, A010051, A001105.

a046920 n = length $ filter ((\x -> x == 1 || a010051 x == 1) . (n -)) $
                            takeWhile (< n) a001105_list
-- Reinhard Zumkeller, Apr 03 2013

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A046921 Number of ways to express 2n+1 as p+2a^2; p = 1 or prime, a >= 0.

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A046923 Number of ways to express 2n+1 as p+2a^2; p prime, a >= 0.

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A046920 Number of ways to express n as p+2a^2; p = 1 or prime, a >= 0.

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