A322155 Consecutive terms that appear more than once in A014237.

-1, 5, 13, 41, 67, 131, 167, 191, 199, 319, 433, 503, 667, 685, 835, 859, 1033, 1565, 1645, 2087, 2695, 2969, 3199, 3329, 3743, 3949, 4135, 4625, 4639, 4831, 5549, 5629, 5663, 5741, 5807, 6031, 6749, 7171, 7543, 8621, 8773, 9161, 9293, 10049, 10333, 11773, 12061, 13057

Offset: 1

Author

Enrique Navarrete, Dec 11 2018

Keywords

• sign

Comments

The only term that appears three times is -1, while all other terms appear twice (looking up to n = 10000 in A014237).

Conjecture: the sequence is infinite.

Examples

			-1 is in the sequence since it appears three consecutive times in A014237 (at n = 2, 3, 4).
5 is in the sequence since it appears two consecutive times in A014237 (at n = 7, 8).
		

Crossrefs

Cf. A000040, A014237, A018252.

Programs

Mathematica

nonPrime[n_] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n];  diff[n_] := Prime[n] - nonPrime[n]; s={}; d1=0; n=3; While[Length[s] < 50, d2 = diff[n]; n++; If[d2 == d1, AppendTo[s, d1]]; d1 = d2]; s (* Amiram Eldar, Dec 12 2018 *)

PARI

nextcomp(c) = {while(isprime(c), c++); c;}
lista(nn) = {my(p = 2, c = 1, d, v = vector(nn)); for (n=1, nn, v[n] = p - c; p = nextprime(p+1); c = nextcomp(c+1);); my(last = v[1], nb = 1); for (n=2, nn, if (v[n] == last, nb++, if (nb > 1, print1(last, ", ")); last = v[n]; nb = 1););} \\ Michel Marcus, Dec 20 2018