A096974 Numbers n such that A096123(n) = n!/(nextprime(n/2)-1)!.

1, 2, 3, 5, 8, 9, 11, 12, 13, 20, 21, 24, 25, 32, 33, 36, 37, 44, 45, 54, 55, 56, 57, 60, 61, 72, 73, 80, 81, 83, 84, 85, 92, 93, 104, 105, 116, 117, 120, 121, 130, 131, 132, 133, 140, 141, 144, 145, 156, 157, 164, 165, 176, 177, 192, 193, 200, 201, 204, 205, 212, 213

Offset

1,2

Comments

Suggested by the apparently false conjecture (A. Murthy) that A096123(n) = n!/(nextprime(n/2)-1)! for all sufficiently large n.

Observation: If n is an even term then n+1 is also a term. Odd terms n that are not preceded by term n-1 are very rare; only 1, 5, 11, 83, 455, 623, 839, 1139, 1199, 2039, 2459, 2579, 2639, 2855, 2975 have been found up to 3000.

Links

Table of n, a(n) for n=1..62.

Example

A096123(11) = 11!/(nextprime(11/2)-1)! = 11!/(6-1)! = 55440, hence 11 is a term.

Prog

(PARI) {for(n=1, 215, p=1; k=0; b=1; while(b&&k<n, p=p*(n-k); d=(n-k)!; if(p%d==0, b=0; if(p==n!/(nextprime(n/2)-1)!, print1(n, ", ")), k++)))}

Crossrefs

Cf. A096123.

Sequence in context: A047372 A308469 A247547 * A286486 A285092 A027756

Adjacent sequences: A096971 A096972 A096973 * A096975 A096976 A096977

Keyword

nonn

Author

Klaus Brockhaus, Jul 17 2004

Status

approved