The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280917 Expansion of 1/(1 - x - Sum_{k>=1} x^prime(k)). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of compositions (ordered partitions) of n into prime parts (1 included) (A008578). LINKS Indranil Ghosh, Table of n, a(n) for n = 0..99 FORMULA G.f.: 1/(1 - x - Sum_{k>=1} x^prime(k)). EXAMPLE 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]. MATHEMATICA nmax = 39; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x] PROG (PARI) Vec(1 / (1 - x - sum(k=1, 100,  x^prime(k))) + O(x^100)) \\ Indranil Ghosh, Mar 09 2017 CROSSREFS Cf. A000607, A002124, A008578, A023360, A034891, A036497. Sequence in context: A287154 A024502 A280254 * A052535 A027988 A238859 Adjacent sequences:  A280914 A280915 A280916 * A280918 A280919 A280920 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 10 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 1 03:24 EDT 2020. Contains 337441 sequences. (Running on oeis4.)