login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A207325
Primes p which divide A003499((p-1)/2)+6 and do not divide A003499(n) + 6 where n < (p-1)/2.
0
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
1,1
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.
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 *)
CROSSREFS
Cf. A003499, A001541 (which equals 1/2 of A003499).
Sequence in context: A152871 A329760 A156221 * A295243 A179017 A078971
KEYWORD
nonn
AUTHOR
Kenneth J Ramsey, Feb 16 2012
STATUS
approved