A092970 -id:A092970 - cp's OEIS frontend

A092068 Positions of 0's in A092970.

Original entry on oeis.org

18, 51, 53, 84, 95, 100, 104, 106, 143, 178, 180, 181, 188

Offset: 1

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004

nonn

Cf. A092970.

A092969 a(1) = 2; for n>1, a(n) = largest prime of the form n!/k + 1, where k < n, or 0 if no such prime exists.

Original entry on oeis.org

2, 3, 7, 13, 61, 241, 2521, 20161, 72577, 604801, 39916801, 59875201, 3113510401, 17435658241, 186810624001, 10461394944001, 118562476032001, 0, 24329020081766401, 304112751022080001, 12772735542927360001

Offset: 1

Amarnath Murthy, Mar 26 2004

nonn

Conjecture: There are only finitely many zeros in this sequence. In other words the sequence is identical to A092965 barring a finite set of terms which are zero.

I found zeros for n: 18,51,53,84,95,100,104,106,143,178,180,181,188,202,203,(204). - Robert G. Wilson v, Mar 27 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A092968, A092970.

f[n_] := Block[{k = 1}, While[ !PrimeQ[n!/k + 1], k++ ]; If[k < n, n!/k + 1, 0]]; Table[ f[n], {n, 22}] (* Robert G. Wilson v, Mar 27 2004 *)

a(n)=for (i=1,n,if(isprime(n!/i+1),return((n!/i+1))))

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 26 2004

A206762 a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 2, 5, 6, 1, 8, 2, 5, 7, 2, 3, 0, 5, 8, 4, 16, 3, 8, 4, 10, 1, 13, 8, 2, 19, 4, 11, 11, 7, 3, 1, 12, 13, 4, 1, 24, 2, 8, 5, 9, 25, 16, 2, 12, 0, 26, 0, 17, 22, 44, 22, 37, 7, 48, 4, 37, 18, 7, 39, 16, 19, 7, 15, 19, 36, 30, 1, 14, 15, 16, 1

Offset: 2

Vladimir Shevelev, Feb 12 2012

nonn

The sequence of primes n!/a(n)+1, when a(n)>0, is increasing.

Cf. A089136, A092265, A092965, A092969, A092970.

Table[s = Select[Range[n - 1], PrimeQ[n!/# + 1] &, 1]; If[s == {}, 0, s[[1]]], {n, 2, 100}] (* T. D. Noe, Feb 13 2012 *)

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A092068 Positions of 0's in A092970.

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A092969 a(1) = 2; for n>1, a(n) = largest prime of the form n!/k + 1, where k < n, or 0 if no such prime exists.

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A206762 a(n) is the least number from 1,2,...,n-1, such that n!/a(n)+1 is prime, and a(n)=0, if such number does not exist.

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