A195507 Smallest integer m greater than n such that m (mod k) == n (mod k) for k = 1..n-1.

2, 3, 5, 10, 17, 66, 67, 428, 849, 2530, 2531, 27732, 27733, 360374, 360375, 360376, 720737, 12252258, 12252259, 232792580, 232792581, 232792582, 232792583, 5354228904, 5354228905, 26771144426, 26771144427, 80313433228, 80313433229, 2329089562830

Offset

1,1

Comments

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.)

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

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = n + A003418(n-1). - Franklin T. Adams-Watters, Sep 20 2011

Crossrefs

Cf. A003418.

Sequence in context: A259393 A018163 A339293 * A117222 A199594 A081172

Adjacent sequences: A195504 A195505 A195506 * A195508 A195509 A195510

Keyword

nonn

Author

John W. Layman, Sep 19 2011

Status

approved