Revision History for A280917
(Underlined text is an addition;
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Showing entries 1-10
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#11 by N. J. A. Sloane at Thu Mar 09 14:48:35 EST 2017
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#10 by Joerg Arndt at Thu Mar 09 12:32:40 EST 2017
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#9 by Joerg Arndt at Thu Mar 09 12:32:25 EST 2017
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(PARI) print(Vec(1 / (1 - x - sum(k=1, 100, x^prime(k))) + O(x^100))); )) \\ _Indranil Ghosh_, Mar 09 2017
\\ Indranil Ghosh, Mar 09 2017
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proposed
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Discussion
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| Thu Mar 09
| 12:32
| Joerg Arndt: Useless use of "print". Fixed.
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#8 by Indranil Ghosh at Thu Mar 09 12:24:14 EST 2017
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#7 by Indranil Ghosh at Thu Mar 09 12:23:31 EST 2017
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(PARI) aprint(Vec(1 / (1 - x) = - sum(k=1, 100, x^prime(k)); ))) + O(x^100)));
print(Vec(1 / (1 - x - a(x)) + O(x^100))); \\ Indranil Ghosh, Mar 09 2017
\\ Indranil Ghosh, Mar 09 2017
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#6 by Indranil Ghosh at Thu Mar 09 12:21:12 EST 2017
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#5 by Indranil Ghosh at Thu Mar 09 12:19:48 EST 2017
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| LINKS
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Indranil Ghosh, <a href="/A280917/b280917.txt">Table of n, a(n) for n = 0..99</a>
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| PROG
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(PARI) a(x) = sum(k=1, 100, x^prime(k));
print(Vec(1 / (1 - x - a(x)) + O(x^100))); \\ Indranil Ghosh, Mar 09 2017
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approved
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#4 by N. J. A. Sloane at Wed Jan 11 03:23:49 EST 2017
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#3 by Ilya Gutkovskiy at Tue Jan 10 16:30:55 EST 2017
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#2 by Ilya Gutkovskiy at Tue Jan 10 16:21:55 EST 2017
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| NAME
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allocated for Ilya Gutkovskiy
Expansion of 1/(1 - x - Sum_{k>=1} x^prime(k)).
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| DATA
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1, 1, 2, 4, 7, 14, 26, 50, 95, 180, 343, 652, 1240, 2359, 4486, 8532, 16227, 30862, 58697, 111636, 212321, 403814, 768015, 1460691, 2778094, 5283667, 10049027, 19112282, 36349721, 69133673, 131485594, 250072951, 475614693, 904573387, 1720411555, 3272057256, 6223138101, 11835809946, 22510571803, 42812941849
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| OFFSET
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0,3
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| COMMENTS
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Number of compositions (ordered partitions) of n into prime parts (1 included) (A008578).
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| LINKS
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<a href="/index/Com#comp">Index entries for sequences related to compositions</a>
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| FORMULA
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G.f.: 1/(1 - x - Sum_{k>=1} x^prime(k)).
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| EXAMPLE
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a(4) = 7 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
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| MATHEMATICA
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nmax = 39; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x]
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| CROSSREFS
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Cf. A000607, A002124, A008578, A023360, A034891, A036497.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Ilya Gutkovskiy, Jan 10 2017
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approved
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