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A291504 Number of permutations s_1,s_2,...,s_n of 1,2,...,n such that for all j=1,2,...,n, Sum_{i=1..j} s_i is not a prime. 0
1, 1, 0, 1, 3, 8, 48, 206, 1838, 13336, 133764, 1081556, 11046816, 108196128, 1555323224, 16279258144, 289771660328, 3495882548784, 66923393467216, 942785369844048, 15625264115770992, 315553823251866304, 5974132307015712032, 104979988889030774848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..23.

EXAMPLE

1             is not a prime,

1 + 3         is not a prime,

1 + 3 + 2     is not a prime,

1 + 3 + 2 + 4 is not a prime.

So [1, 3, 2, 4] satisfies all the conditions.

---------------------------------------------

a(1) = 1: [[1]];

a(3) = 1: [[1, 3, 2]];

a(4) = 3: [[1, 3, 2, 4], [1, 3, 4, 2], [4, 2, 3, 1]];

a(5) = 8: [[1, 3, 2, 4, 5], [1, 3, 4, 2, 5], [1, 5, 2, 4, 3], [1, 5, 4, 2, 3], [4, 2, 3, 1, 5], [4, 2, 3, 5, 1], [4, 5, 1, 2, 3], [4, 5, 3, 2, 1]].

MATHEMATICA

Table[Count[Permutations@ Range@ n, _?(AllTrue[Accumulate@ #, ! PrimeQ@ # &] &)], {n, 0, 10}] (* Michael De Vlieger, Aug 26 2017 *)

CROSSREFS

Cf. A067957, A291355.

Sequence in context: A210373 A247033 A309578 * A034183 A003216 A146161

Adjacent sequences:  A291501 A291502 A291503 * A291505 A291506 A291507

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 25 2017

EXTENSIONS

a(0), a(12)-a(23) from Alois P. Heinz, Aug 25 2017

STATUS

approved

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Last modified July 31 15:25 EDT 2021. Contains 346374 sequences. (Running on oeis4.)