A090851 Smallest positive k such that phi(2n*k+1) < phi(2n*k), where phi is Euler's totient function.

157, 131, 41449509748313314446079881572662251904099551759079570289, 103, 87200213, 23228416536806454739917249069243610966391359542839893417, 28651, 59, 16202086544304724831441296633918338274264333181606642583

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..9.

Greg Martin, The smallest solution of phi(30n+1) < phi(30n) is ..., arXiv:math/0904025, 1998.

D. J. Newman, Euler's phi function on arithmetic progressions, Amer. Math. Monthly, Vol. 104, No. 3 (Mar. 1997), pp. 256-257.

Herman te Riele, On the size of solutions of the inequality phi(ax+b) < phi(ax)

Crossrefs

Cf. A090849 (least k such that phi(1+k*2^n) <= phi(k*2^n)).

Sequence in context: A239338 A028675 A248504 * A045230 A180551 A096704

Adjacent sequences: A090848 A090849 A090850 * A090852 A090853 A090854

Keyword

nonn

Author

T. D. Noe, Dec 09 2003

Extensions

Replaced arXiv URL by non-cached version - R. J. Mathar, Oct 30 2009

Status

approved