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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.
3
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
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
KEYWORD
nonn
AUTHOR
Bernard Schott, Dec 13 2020
STATUS
approved