OFFSET
1,1
COMMENTS
From Bernard Schott, Dec 14 2020: (Start)
Equivalently, primes p such that the ratio (p-1)/gpf(p-1) = 2^k where gpf(m) is the greatest prime factor of m, A006530.
Paul Erdős asked if there are infinitely many primes p in this sequence (see R. K Guy reference). (End)
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B46, p. 154.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..2000
Graeme L. Cohen, On a conjecture of Makowski and Schinzel, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8.
EXAMPLE
3 = 2*2^0+1 is a term and 2/2 = 1 = 2^0.
7 = 3*2^1+1 is a term and 6/3 = 2 = 2^1.
13 = 3*2^2+1 is a term and 12/3 = 4 = 2^2.
41 = 5*2^3+1 is a term and 40/5 = 8 = 2^3.
113 = 7*2^4+1 is a term and 112/7 = 16 = 2^4.
MAPLE
alias(pf = NumberTheory:-PrimeFactors): gpf := n -> max(pf(n)):
is_a := n -> isprime(n) and pf((n-1)/gpf(n-1)) = {2}:
3, op(select(is_a, [$3..919])); # Peter Luschny, Dec 14 2020
MATHEMATICA
Select[Range[3, 1000], PrimeQ[#] && !CompositeQ[(# - 1)/2^IntegerExponent[(# - 1), 2]] &] (* Amiram Eldar, Dec 28 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
STATUS
approved