A207325 Primes p which divide A003499((p-1)/2)+6 and do not divide A003499(n) + 6 where n < (p-1)/2.

3, 5, 11, 13, 19, 37, 43, 53, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 181, 211, 277, 283, 307, 317, 331, 347, 349, 373, 397, 421, 461, 467, 491, 499, 509, 523, 541, 547, 557, 563, 571, 587, 613, 619, 653, 659, 661, 691, 701, 709, 733, 739

Offset: 1

Author

Kenneth J Ramsey, Feb 16 2012

Keywords

• nonn

Comments

All odd numbers less than 3,000,000 have been checked and it appears that most primes of the form 8N +/- 3 (e.g. 3,5,11,13,19,37 ...) meet the test with some exceptions, (e.g. 29) and no primes of the form 8N +/-1 or composites meet the test.

Crossrefs

Cf. A003499, A001541 (which equals 1/2 of A003499).

Programs

Mathematica

f=Compile[{{Co,_Integer}, {S0,_Integer}, {S1,_Integer}, {Caa,_Integer}}, Module[{xCo=Co, xS0=S0, xS1=S1, Temp}, While[Temp=Mod[6 xS1-xS0-6, Caa]; xCo>0 && Temp>0, xS0=xS1; xS1=Temp; xCo--]; xCo]]; Caa=5; Reap[While[Caa<1000, Co=(Caa-3)/2; S0=2; S1=3; If[f[Co, S0, S1, Caa] == 1, Sow[Caa]]; Caa+=2]] (* prime 3 skipped to simplify code. The above code, provided by Bill Simpson, is 20 times faster than my original code. Note that it also appears possible to increase speed by a factor of 10 by not searching numbers of the form 8n+/-1 *)