A288244 Numbers k such that prime(k)*prime(k+1)*prime(k+2) mod prime(k+3) is even.

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

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

Table of n, a(n) for n=1..63.

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