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%I #16 Dec 15 2020 16:24:01
%S 71,101,131,191,251,281,311,401,431,461,521,701,761,821,881,941,971,
%T 1031,1061,1091,1151,1181,1301,1361,1451,1481,1511,1571,1601,1721,
%U 1811,1901,1931,2081,2111,2141,2351,2411,2441,2621,2711,2741,2801,3041,3251,3371
%N 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.
%C 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)
%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B46, p. 154.
%H Robert Israel, <a href="/A339463/b339463.txt">Table of n, a(n) for n = 1..10000</a>
%e 41 is prime, 40/5 = 8 = 2^3, hence 41 is not a term.
%e 101 is prime, 100/5 = 20 = 2^2 * 5, hence 101 is a term.
%e 491 is prime, 490/7 = 70 = 2 * 5 * 7, hence 491 is not a term.
%e 521 is prime, 520/13 = 40 = 2^3 * 5, hence 521 is a term.
%p alias(pf = NumberTheory:-PrimeFactors): gpf := n -> max(pf(n)):
%p is_a := n -> isprime(n) and pf((n-1)/gpf(n-1)) = {2, 5}:
%p select(is_a, [$5..3371]); # _Peter Luschny_, Dec 13 2020
%t 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 *)
%Y Cf. A006093 (prime(n)-1), A006530, A052126, A339464.
%Y Cf. A074781 (ratio=2^k), A339465 (ratio=2^q*3^r).
%Y Subsequence of A132232 and of A339466.
%K nonn
%O 1,1
%A _Bernard Schott_, Dec 13 2020
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