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A252282 Intersection of A251964 and A252280. 7
2, 5, 7, 11, 19, 37, 41, 61, 71, 73, 101, 109, 127, 163, 181, 211, 241, 271, 307, 313, 383, 421, 433, 523, 541, 587, 601, 613, 631, 811, 947, 971, 983, 1013, 1031, 1033, 1063, 1123, 1153, 1171, 1201, 1229, 1303, 1423, 1483, 1531, 1621, 1973, 2053, 2113, 2207, 2311, 2341 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a prime p, denote by s(p,k) the odd part of the digital sum of p^k. Let, for the first time, s(p,k) be divisible of 5 for k=k_1 and be divisible of 7 for k=k_2.

Sequence lists primes p for which s(p,k_1)=5 and s(p,k_2)=7.

LINKS

Table of n, a(n) for n=1..53.

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; Select[Range[2400],  PrimeQ[#] && okQ[#, 5] && okQ[#, 7] &] (* Amiram Eldar, Dec 08 2018 *)

PROG

(PARI) s(p, k) = my(s=sumdigits(p^k)); s >> valuation(s, 2);

f5(p) = my(k=1); while(s(p, k) % 5, k++); k;

isok5(p) = s(p, f5(p)) == 5;

f7(p) = my(k=1); while(s(p, k) % 7, k++); k;

isok7(p) = s(p, f7(p)) == 7;

lista(nn) = forprime(p=2, nn, if (isok5(p) && isok7(p), print1(p, ", "))); \\ Michel Marcus, Dec 08 2018

CROSSREFS

Cf. A221858, A225039, A225093, A251964, A252280, A252281.

Sequence in context: A252280 A184774 A038884 * A040122 A318207 A038955

Adjacent sequences:  A252279 A252280 A252281 * A252283 A252284 A252285

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Dec 16 2014

EXTENSIONS

More terms from Michel Marcus, Dec 08 2018

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)