A339463 Primes p such that (p-1)/gpf(p-1) = 2^q * 5^r with q, r >= 1, where gpf(m) is the greatest prime factor of m, A006530.

71, 101, 131, 191, 251, 281, 311, 401, 431, 461, 521, 701, 761, 821, 881, 941, 971, 1031, 1061, 1091, 1151, 1181, 1301, 1361, 1451, 1481, 1511, 1571, 1601, 1721, 1811, 1901, 1931, 2081, 2111, 2141, 2351, 2411, 2441, 2621, 2711, 2741, 2801, 3041, 3251, 3371

Offset

1,1

Comments

These primes that are all congruent to 11 (mod 30) form a subsequence of A132232. The first terms of A132232 that are not terms here are 11, 41, 491, ... (see examples)

References

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B46, p. 154.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

41 is prime, 40/5 = 8 = 2^3, hence 41 is not a term.
101 is prime, 100/5 = 20 = 2^2 * 5, hence 101 is a term.
491 is prime, 490/7 = 70 = 2 * 5 * 7, hence 491 is not a term.
521 is prime, 520/13 = 40 = 2^3 * 5, hence 521 is a term.

Maple

alias(pf = NumberTheory:-PrimeFactors): gpf := n -> max(pf(n)):
is_a := n -> isprime(n) and pf((n-1)/gpf(n-1)) = {2, 5}:
select(is_a, [$5..3371]); # Peter Luschny, Dec 13 2020

Mathematica

q[n_] := Divisible[n, 10] && ((PrimeQ[(r = n/2^IntegerExponent[n, 2]/5^(e = IntegerExponent[n, 5]))] && r > 5) || (r == 1 && e > 1)); Select[Range[3500], PrimeQ[#] && q[# - 1] &] (* Amiram Eldar, Dec 13 2020 *)

Crossrefs

Cf. A006093 (prime(n)-1), A006530, A052126, A339464.

Cf. A074781 (ratio=2^k), A339465 (ratio=2^q*3^r).

Subsequence of A132232 and of A339466.

Sequence in context: A234962 A166252 A339466 * A166576 A369250 A195270

Adjacent sequences: A339460 A339461 A339462 * A339464 A339465 A339466

Keyword

nonn

Author

Bernard Schott, Dec 13 2020

Status

approved