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Search: a046922 -id:a046922
Displaying 1-3 of 3 results found. page 1
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A046921 Number of ways to express 2n+1 as p+2a^2; p = 1 or prime, a >= 0. +10
8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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
LINKS
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
FORMULA
a(n) = A046920(A005408(n)). - Reinhard Zumkeller, Apr 03 2013
PROG
(Haskell)
a046921 = a046920 . a005408 -- Reinhard Zumkeller, Apr 03 2013
CROSSREFS
Cf. A042978, A046920, A046922, A046923, A060003, A143539.
Cf. A007697.
KEYWORD
nonn
AUTHOR
David W. Wilson
STATUS
approved
A046923 Number of ways to express 2n+1 as p+2a^2; p prime, a >= 0. +10
7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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
LINKS
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
PROG
(Haskell)
a046923 = a046922 . a005408 -- Reinhard Zumkeller, Apr 03 2013
CROSSREFS
Cf. A042978, A046920, A046921, A046922, A060003, A143539
KEYWORD
nonn
AUTHOR
David W. Wilson
EXTENSIONS
Definition corrected by T. D. Noe, Aug 23 2008
STATUS
approved
A046920 Number of ways to express n as p+2a^2; p = 1 or prime, a >= 0. +10
6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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.
Index entries for sequences related to Goldbach conjecture
PROG
(Haskell)
a046920 n = length $ filter ((\x -> x == 1 || a010051 x == 1) . (n -)) $
takeWhile (< n) a001105_list
-- Reinhard Zumkeller, Apr 03 2013
CROSSREFS
Cf. A042978, A046921, A046922, A046923, A060003, A143539.
Cf. A016067, A008578, A010051, A001105.
KEYWORD
nonn
AUTHOR
David W. Wilson
STATUS
approved
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Last modified August 29 23:34 EDT 2024. Contains 375520 sequences. (Running on oeis4.)