A252732 In view of their definitions, let us refer to A251964 as sequence "5", A252280 as sequence "7", and similarly define sequence "prime(n)"; a(n) is the third term of the intersection of sequences "5", ..., "prime(n)".

7, 7, 7, 7, 421, 2311, 43321, 59730109, 537052693

Offset

3,1

Comments

Is this sequence finite?

Up to n=13, the first two terms of the intersection of sequences "5", ..., "prime(n)" are 2 and 5 respectively.

Links

Table of n, a(n) for n=3..11.

Mathematica

s[p_, k_] := Module[{s = Total[IntegerDigits[p^k]]}, s/2^IntegerExponent[s, 2]]; f[p_, q_] := Module[{k = 1}, While[ ! Divisible[s[p, k], q], k++]; k]; okQ[p_, q_] := s[p, f[p, q]] == q; okpQ[p_, nbseq_] := Module[{ans=True}, Do[If[!okQ[p, Prime[k+2]], ans=False; Break[]], {k, 1, nbseq}]; ans]; a[n_]:=Module[{c=0, p=2}, While[c<3 , If[okpQ[p, n], c++]; p=NextPrime[p]]; NextPrime[p, -1]]; Array[a, 6] (* Amiram Eldar, Dec 09 2018 *)

Prog

(PARI) s(p, k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);
f(p, vp) = my(k=1); while(s(p, k) % vp, k++); k;
isok(p, vp) = s(p, f(p, vp)) == vp;
isokp(p, nbseq) = {for (k=1, nbseq, if (! isok(p, prime(k+2)), return (0)); ); return (1); }
a(n) = {my(nbpok = 0); forprime(p=2, oo, if (isokp(p, n), nbpok ++); if (nbpok == 3, return (p)); ); } \\ Michel Marcus, Dec 09 2018

Crossrefs

Cf. A251964, A252280, A252281, A252282, A252283, A252666, A252668, A252670.

Sequence in context: A084503 A168292 A024733 * A360807 A011472 A246506

Adjacent sequences: A252729 A252730 A252731 * A252733 A252734 A252735

Keyword

nonn,base,more

Author

Vladimir Shevelev, Dec 21 2014

Extensions

More terms from Peter J. C. Moses, Dec 21 2014

a(10)-a(11) from Michel Marcus, Dec 09 2018

Status

approved