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A103151
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Number of decompositions of 2n+1 into 2p+q, where p and q are both odd primes (A065091).
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9
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0, 0, 0, 1, 1, 2, 1, 3, 2, 2, 2, 3, 3, 4, 2, 4, 2, 4, 4, 4, 4, 5, 3, 4, 6, 5, 3, 6, 3, 3, 6, 6, 5, 7, 3, 4, 7, 6, 5, 8, 3, 7, 7, 7, 4, 10, 5, 6, 9, 5, 5, 11, 5, 6, 9, 7, 6, 10, 7, 5, 11, 8, 6, 10, 5, 6, 12, 8, 5, 12, 5, 9, 12, 8, 6, 13, 7, 6, 11, 9, 9, 16, 4, 8, 12, 9, 9, 13, 7, 6, 13, 11, 8, 16, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Conjecture: all items for n>=4 are greater than or equal to 1. This is a stronger conjecture than the Goldbach conjecture.
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EXAMPLE
| For 2*4+1 = 9 we have just one such composition: 9 = 2*3+3, so a(4)=1;
For 2*14+1 = 29 we have four such compositions: 29 = 2*3+23 = 2*5+19 = 2*11+7 = 2*13+3, so a(14)=4.
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MATHEMATICA
| Do[m = 3; ct = 0; While[(m*2) < n, If[PrimeQ[m], cp = n - (2*m); If[ PrimeQ[cp], ct = ct + 1]]; m = m + 2]; Print[ct], {n, 9, 299, 2}]
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PROG
| (Scheme, with Aubrey Jaffer's SLIB Scheme library from http://www.swiss.ai.mit.edu/~jaffer/SLIB.html )
(define (A103151 n) (let loop ((i 2) (z 0)) (let ((p1 (A000040 i))) (cond ((>= p1 n) z) ((prime? (+ 1 (* 2 (- n p1)))) (loop (+ 1 i) (+ 1 z))) (else (loop (+ 1 i) z))))))
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CROSSREFS
| A001031, A103152.
Sequence in context: A057514 A140720 A033559 * A035221 A035191 A177062
Adjacent sequences: A103148 A103149 A103150 * A103152 A103153 A103154
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KEYWORD
| nonn
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AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 09 2005
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EXTENSIONS
| Edited and Scheme-code added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jun 19 2007
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