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%I #18 May 07 2020 05:24:13
%S 2,3,5,10,17,66,67,428,849,2530,2531,27732,27733,360374,360375,360376,
%T 720737,12252258,12252259,232792580,232792581,232792582,232792583,
%U 5354228904,5354228905,26771144426,26771144427,80313433228,80313433229,2329089562830
%N Smallest integer m greater than n such that m (mod k) == n (mod k) for k = 1..n-1.
%C Conjecture: The sequence (a(n): n >= 1) satisfies the following recurrence. Write a(n)/n in lowest terms as num/d. Then a(n+1) = d*a(n) - (d-1)*n + 1. Illustration: a(4) = 10 and a(4)/4 = 5/2 in lowest terms. Then a(5) = 2*10 - 1*4 + 1 = 17. (This has been verified up to a(23) = 232792583.)
%C This follows from the formula below. The value d is 1 unless n is a prime power p^k, in which case it is p. - _Franklin T. Adams-Watters_, Sep 20 2011
%F a(n) = n + A003418(n-1). - _Franklin T. Adams-Watters_, Sep 20 2011
%Y Cf. A003418.
%K nonn
%O 1,1
%A _John W. Layman_, Sep 19 2011