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 A288244 Numbers k such that prime(k)*prime(k+1)*prime(k+2) mod prime(k+3) is even. 0
 1, 2, 3, 5, 10, 11, 12, 13, 14, 15, 18, 19, 20, 24, 28, 31, 34, 36, 37, 39, 40, 41, 42, 45, 46, 48, 49, 57, 64, 66, 67, 68, 70, 72, 73, 75, 78, 79, 82, 83, 86, 89, 90, 92, 93, 95, 96, 97, 99, 100, 103, 105, 108, 109, 110, 116, 117, 120, 121, 124, 125, 126, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(971)=325850. No more terms? Almost surely the above conjecture is true, but it is currently hopeless to prove. It would follow from prime gaps being less than about the cube root, but this is not known even under RH. - Charles R Greathouse IV, Jun 10 2017 LINKS MATHEMATICA Select[Range@ 128, EvenQ@ Mod[Times @@ Take[#, 3], #[[4]]] &@ Prime[# + Range[0, 3]] &] (* Michael De Vlieger, Jun 09 2017 *) Position[Partition[Prime[Range[140]], 4, 1], _?(EvenQ[Mod[Times@@Take[#, 3], #[[4]]]]&)]//Flatten//Quiet (* Harvey P. Dale, Oct 14 2020 *) PROG (PARI) isok(n) = (((prime(n)*prime(n+1)*prime(n+2)) % prime(n+3)) % 2) == 0; \\ Michel Marcus, Jun 07 2017 (PARI) list(lim)=my(v=List(), p=2, q=3, r=5, n); forprime(s=7, , if(n++>lim, break); if(p*q*r%s%2==0, listput(v, n)); p=q; q=r; r=s); Vec(v) \\ Charles R Greathouse IV, Jun 10 2017 CROSSREFS Sequence in context: A038807 A094542 A175481 * A246392 A219860 A076681 Adjacent sequences:  A288241 A288242 A288243 * A288245 A288246 A288247 KEYWORD nonn AUTHOR Zak Seidov, Jun 06 2017 STATUS approved

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Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)