cp's OEIS Frontend

A001259 A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.

%I A001259 M2423 N0958 #37 Mar 19 2021 06:58:30
%S A001259 3,5,7,17,19,37,97,113,257,401,487,631,971,1297,1801,19457,22051,
%T A001259 28817,65537,157303,160001
%N A001259 A sequence of sorted odd primes 3 = p_1 < p_2 < ... < p_m such that p_i-2 divides the product p_1*p_2*...*p_(i-1) of the earlier primes and each prime factor of p_i-1 is a prime factor of twice the product.
%C A001259 Old name was: A special sequence of primes.
%C A001259 Holt shows this sequence is complete. - _T. D. Noe_, Jul 28 2005
%C A001259 This sequence was used by Schinzel (1958) and Schinzel and Wakulicz (1959) to prove that there are at least two solutions k to phi(n+k) = phi(k) for all n <= 8*10^47 and 2*10^58, respectively. - _Amiram Eldar_, Mar 19 2021
%D A001259 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001259 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001259 Jeffery J. Holt, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01509-6">The minimal number of solutions to phi(n)=phi(n+k)</a>, Math. Comp., 72 (2003), 2059-2061.
%H A001259 A. Schinzel and Andrzej Wakulicz, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa4/aa431.pdf">Sur l'équation phi(x+k)=phi(x), I.</a>, Acta Arith. 4 (1958), 181-184. - _Jonathan Sondow_, Oct 07 2012
%H A001259 A. Schinzel and Andrzej Wakulicz; <a href="http://pldml.icm.edu.pl/mathbwn//element/bwmeta1.element.bwnjournal-article-aav5i4p425bwm">Sur l'équation phi(x+k)=phi(x). II</a>. Acta Arith. 5 1959 425-426.
%Y A001259 Cf. A007015, A342701.
%K A001259 nonn,fini,full
%O A001259 1,1
%A A001259 _N. J. A. Sloane_
%E A001259 New name, giving a definition, by _Jonathan Sondow_, Oct 06 2012