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A103152
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Smallest odd number which can be written as a sum 2p+q (where p and q are both odd primes, A065091) in exactly n ways, zero if there are no such odd number.
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6
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9, 13, 17, 29, 45, 51, 69, 81, 99, 93, 105, 135, 153, 201, 195, 165, 231, 237, 321, 297, 225, 363, 725, 393, 285, 315, 471, 483, 435, 405, 465, 561, 555, 495, 609, 783, 675, 867, 849, 963, 645, 525, 693, 897, 795, 915, 987, 735, 855, 825, 765, 1095, 975, 1467
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: except for the 2nd, 3rd and 4th terms, all other terms are divisible by 3; See also comments in A103151.
a(23)=725 is also not divisible by 3. [From D. S. McNeil (mcneil(AT)hku.hk), Sep 06 2010]
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EXAMPLE
| 9 is the smallest odd number with just one such composition: 9 = 3+2*3, thus a(1)=9.
Similarly, 13 is smallest with exactly 2 compositions: 13 = 3+2*5 = 7+2*3, thus a(2)=13.
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MATHEMATICA
| Array[a, 300]; Do[a[n] = 0, {n, 1, 300}]; n = 9; ct = 0; While[ct < 200, m = 3; ct = 0; While[(m*2) < n, If[PrimeQ[m], cp = n - (2* m); If[PrimeQ[cp], ct = ct + 1]]; m = m + 2]; If[a[ct] == 0, a[ct] = n]; n = n + 2]; Print[a]
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PROG
| (Scheme:) (define (A103152 n) (+ 1 (* 2 (first-n-where-fun_n-is-i1 A103151 n))))
(define (first-n-where-fun_n-is-i1 fun i) (let loop ((n 1)) (cond ((= i (fun n)) n) (else (loop (+ n 1))))))
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CROSSREFS
| A103151, A001172, A001031.
Sequence in context: A134441 A174055 A188220 * A090415 A026283 A026045
Adjacent sequences: A103149 A103150 A103151 * A103153 A103154 A103155
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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, Scheme-code added and starting offset changed from 0 to 1 by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jun 19 2007
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