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

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

Author

Derek Orr, Aug 01 2014

Keywords

• nonn

Comments

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

Crossrefs

Cf. A240161, A240163.

Programs

PARI

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++)