A240161 -id:A240161 - cp's OEIS frontend

A240160 Least number k such that (k!-n)/k is prime, or 0 if no such k exists.

0, 0, 0, 4, 5, 0, 7, 8, 0, 0, 0, 4, 13, 0, 15, 4, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 31, 0, 33, 34, 5, 0, 0, 0, 39, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 6, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5

Offset: 1

Derek Orr, Aug 01 2014

nonn

For a(n) > 0, a(n) is a divisor of n.

If a(n) = n, then n - 1 is in A002982.

Jens Kruse Andersen, Table of n, a(n) for n = 1..2500

Cf. A002982, A240161, A245756.

a(n)=for(k=1,n,s=(k!-n)/k;if(floor(s)==s,if(ispseudoprime(s),return(k))))
vector(150, n, a(n))

Typo in PARI code fixed by Colin Barker, Aug 02 2014

A240164 Numbers n such that (k!+n)/k and (k!-n)/k are prime for some k.

Original entry on oeis.org

4, 25, 35, 42, 65, 66, 85, 95, 102, 114, 121, 133, 152, 170, 186, 204, 222, 259, 279, 282, 296, 318, 328, 333, 354, 366, 376, 438, 451, 462, 469, 474, 536, 539, 546, 583, 584, 603, 618, 623, 642, 654, 678, 682, 707, 721, 749, 833, 856, 931, 938, 963, 1001, 1048, 1062, 1079, 1099, 1141

Offset: 1

Derek Orr, Aug 01 2014

nonn

Subsequence of intersection of A240161 and A240163. [Corrected by Jens Kruse Andersen, Aug 04 2014]

By using Wilson's theorem, we can show that each term of the sequence is composite. - Farideh Firoozbakht, Aug 02 2014

Cf. A240161, A240163.

a(n)=for(k=1,n,s=(k!+n)/k;t=(k!-n)/k;if(floor(s)==s&&floor(t)==t,if(ispseudoprime(s)&&ispseudoprime(t),return(k))))
n=1;while(n<10^3,if(a(n),print1(n,", "));n++)

cp's OEIS Frontend

A240160 Least number k such that (k!-n)/k is prime, or 0 if no such k exists.

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