Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Aug 06 2024 09:03:57
%S 157,131,41449509748313314446079881572662251904099551759079570289,103,
%T 87200213,23228416536806454739917249069243610966391359542839893417,
%U 28651,59,16202086544304724831441296633918338274264333181606642583
%N Smallest positive k such that phi(2n*k+1) < phi(2n*k), where phi is Euler's totient function.
%C Note that a(3) = (5 * 7 * 11 * 13 * 17 * 19 * 23 * ... * 149 - 1) / 6. When 2n is the product of distinct small primes, a(n) is very large; e.g. Martin shows that a(15) is a 1116-digit number. The large values of a(n) were computed quickly using a backtracking algorithm.
%H Greg Martin, <a href="http://arXiv.org/abs/math/9804025">The smallest solution of phi(30n+1) < phi(30n) is ...</a>, arXiv:math/0904025, 1998.
%H D. J. Newman, <a href="http://www.jstor.org/stable/2974791">Euler's phi function on arithmetic progressions</a>, Amer. Math. Monthly, Vol. 104, No. 3 (Mar. 1997), pp. 256-257.
%H Herman te Riele, <a href="https://citeseerx.ist.psu.edu/pdf/6f75bf159f876d71f4fcfbd1cdcba38dfc358c11">On the size of solutions of the inequality phi(ax+b) < phi(ax)</a>
%Y Cf. A090849 (least k such that phi(1+k*2^n) <= phi(k*2^n)).
%K nonn
%O 1,1
%A _T. D. Noe_, Dec 09 2003