A060977 The nonprimes n!+2 ... n!+n are the a(n)-th string of n-1 prime-free consecutive terms, the first such one being the string of composite numbers A000230(k)+1 through A001632(k)-1 when n=2k, or through A001632(k)-2 when n=2k-1.

0, 1, 1, 6, 27, 208, 1755, 16363, 161685, 1736749, 20022517, 250566242, 3359504253

Offset

1,4

Comments

The sequence grows rapidly, like the factorial function.

Links

Table of n, a(n) for n=1..13.

Example

The prime-free sequence 4! + 2 through 4! + 4, i.e., {26, 27, 28}, ranks as the a(4) = 6th triple of consecutive composite numbers, as it comes after {8, 9, 10}, {14, 15, 16}, {20, 21, 22}, {24, 25, 26}, {25, 26, 27}.

Mathematica

Do[ c = 0; a = Table[0, {n - 1} ]; k = 2; While[ k < n! + n + 1, a = Delete[a, 1]; a = Append[a, PrimeQ[k] ]; If[ Union[a] == {False}, c++ ]; k++ ]; Print[c], {n, 2, 12} ]

Crossrefs

Cf. A000230, A001632.

Sequence in context: A092854 A223557 A289022 * A267630 A351737 A047778

Adjacent sequences: A060974 A060975 A060976 * A060978 A060979 A060980

Keyword

more,nonn,nice

Author

Lekraj Beedassy, May 10 2001

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 25 2001

More terms from Robert G. Wilson v, Aug 17 2001

a(13) from Sean A. Irvine, Jan 11 2023

Status

approved