A252670 a(n) is exponential digital index of prime(n).

22, 0, 11, 4, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 1, 0, 0, 5, 0, 2, 0, 0, 1, 0, 0, 0

Offset

1,1

Comments

For the definition of the exponential digital index of a prime p (EDI(p)), see comment in A252668.

Is 22 the maximal term? Is 11 the second maximal term?

Links

Table of n, a(n) for n=1..90.

Formula

a(n)=0, iff n is not in A251964; a(n)=1, iff n is in A251964, but is not A252280;

a(n)=2, iff n is in A251964 & A252980, but is not in A252981, a(n)>=3, iff n is in A251964 & A252980 & A252281.

Prog

(PARI) s(k, pp) = my(sd = sumdigits(pp^k)); sd/2^valuation(sd, 2);
f(n, pp) = {my(p = prime(n), k = 1); while ((sk=s(k, pp)) % p, k++); if (sk == p, k, 0); }
a(n) = {my(pp=prime(n), j=3); while (f(j, pp), j++); j - 3; } \\ Michel Marcus, Dec 09 2018

Crossrefs

Cf. A000040, A251964, A252280, A252281, A252282, A252283, A252666, A252668.

Sequence in context: A023922 A022064 A225343 * A297813 A156462 A040488

Adjacent sequences: A252667 A252668 A252669 * A252671 A252672 A252673

Keyword

nonn,base

Author

Vladimir Shevelev, Dec 20 2014

Extensions

More terms from Michel Marcus, Dec 09 2018

Status

approved