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 A317131 Number of permutations of [n] whose lengths of increasing runs are prime numbers. 7
 1, 0, 1, 1, 5, 19, 80, 520, 2898, 22486, 171460, 1509534, 14446457, 147241144, 1650934446, 19494460567, 248182635904, 3340565727176, 47659710452780, 718389090777485, 11381176852445592, 189580213656445309, 3305258537062221020, 60273557241570401742 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 EXAMPLE a(2) = 1: 12. a(3) = 1: 123. a(4) = 5: 1324, 1423, 2314, 2413, 3412. a(5) = 19: 12345, 12435, 12534, 13245, 13425, 13524, 14235, 14523, 15234, 23145, 23415, 23514, 24135, 24513, 25134, 34125, 34512, 35124, 45123. MAPLE g:= n-> `if`(n=0 or isprime(n), 1, 0): b:= proc(u, o, t) option remember; `if`(u+o=0, g(t),       `if`(g(t)=1, add(b(u-j, o+j-1, 1), j=1..u), 0)+        add(b(u+j-1, o-j, t+1), j=1..o))     end: a:= n-> b(n, 0\$2): seq(a(n), n=0..27); CROSSREFS Cf. A000040, A097597, A218002, A317111, A317128, A317129, A317130, A317132, A317447. Sequence in context: A111929 A146030 A098041 * A149780 A149781 A149782 Adjacent sequences:  A317128 A317129 A317130 * A317132 A317133 A317134 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 21 2018 STATUS approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)