A075468 -id:A075468 - cp's OEIS frontend

A075409 a(n) is the smallest m such that n!-m and n!+m are both primes.

0, 1, 5, 7, 19, 19, 31, 17, 11, 17, 83, 67, 353, 227, 163, 59, 61, 113, 353, 31, 1447, 571, 389, 191, 337, 883, 101, 1823, 659, 709, 163, 1361, 439, 307, 1093, 1733, 2491, 1063, 1091, 1999, 1439, 109, 2753, 607, 2617, 269, 103, 2663, 337, 14447, 2221, 5471, 2887

Offset: 2

Zak Seidov, Sep 18 2002

nonn

For n=3,5,10,21,171,190,348, n! is an interprime, the average of two consecutive primes, see A053709. In general n! may be average of several pairs of primes, in which case the minimal distance is in the sequence. See also n^n and n!! as average of two primes in A075468 and A075410.

According to Goldbach's conjecture, a(n) always exists with a(n) = A047160(n!). - Jens Kruse Andersen, Jul 30 2014

			a(4)=5 because 4!=24 and 19 and 25 are primes with smallest distance 5 from 4!.

Vincenzo Librandi, Table of n, a(n) for n = 2..100

Cf. A033932, A033933, A047160, A053709, A075468, A075410.

smp[n_]:=Module[{m=1,nf=n!},While[!PrimeQ[nf+m]||!PrimeQ[nf-m],m=m+2];m]; Join[{0},Array[smp,60,3]] (* Harvey P. Dale, Apr 18 2014 *)

a(n) = {my (m=0); until (ok, ok = isprime(n!-m) && isprime(n!+m); if (!ok, m++);); return (m);} \\ Michel Marcus, Apr 19 2013

More terms from David Wasserman, Jan 17 2005

A075410 a(n) is the smallest m such that n!!-m and n!!+m are both primes.

Original entry on oeis.org

0, 0, 3, 2, 5, 2, 5, 8, 7, 4, 19, 16, 29, 68, 97, 16, 109, 86, 19, 158, 17, 172, 41, 16, 529, 106, 263, 212, 163, 302, 593, 302, 607, 262, 311, 428, 227, 106, 1271, 8, 229, 386, 1489, 32, 47, 1996, 1097, 2566, 41, 632, 1913, 458, 149, 1244, 2837, 362, 3317, 908

Offset: 2

Zak Seidov, Sep 18 2002

nonn

For n = 5,7,10,11,22,41,67,76,91,96,163,245,299,341, n!! is an interprime, the average of two consecutive primes, see A075275. See also n^n and n! as average of two primes in A075468 and A075409.

			a(4) = 3 because 4!! = 8 and 8 -/+ 3 = 5 and 11 are primes with smallest equal distances from 4!!

Cf. A075275, A075468 and A075409.

smbp[n_]:=Module[{m=0,n2=n!!},While[Total[Boole[PrimeQ[n2+{m,-m}]]] != 2,m++];m]; Array[smbp,60,2] (* Harvey P. Dale, Sep 02 2017 *)

More terms from David Wasserman, Jan 17 2005

A075469 Maximal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.

Original entry on oeis.org

1, 20, 253, 3122, 46651, 823540, 16777155, 387420478, 9999999939, 285311670528, 8916100448227, 302875106592216, 11112006825558003, 437893890380859368, 18446744073709551537, 827240261886336764070, 39346408075296537575383

Offset: 2

Lior Manor, Sep 18 2002

nonn

Are there any negative terms?

Of course the Goldbach conjecture implies that the answer is "no"; further, the first thousand terms are positive. - Charles R Greathouse IV, Mar 16 2016

			a(4) = 253 since 4^4-253 = 3 and 4^4+253 = 509 are both prime.

Charles R Greathouse IV, Table of n, a(n) for n = 2..386

Cf. A075468.

Cf. A000312, A047949.

a(n)=my(N=n^n); forprime(p=2,N, if(isprime(2*N-p), return(N-p))); -1 \\ Charles R Greathouse IV, Mar 16 2016

a(n) = A047949(n^n). - Michel Marcus, Jun 09 2013

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A075409 a(n) is the smallest m such that n!-m and n!+m are both primes.

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A075410 a(n) is the smallest m such that n!!-m and n!!+m are both primes.

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Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A075469 Maximal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.

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Keywords

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