0,3

Also known as Gobel's (or Goebel's) Sequence. Asymptotically, a(n) ~ n*C^(2^n) where C=1.0478... (A115632). A more precise asymptotic formula is given in A116603. - M. F. Hasler, Dec 12 2007

By considering s(n) := n*a(n) mod k, one finds that a(n) is nonintegral iff n>42 - thus this sequence is nonintegral sequence beyond a(42) unless the definition is changed, for example to "integer part of..." or "nearest integer to ...". - M. F. Hasler, Dec 12 2007

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.

T. D. Noe, Table of n, a(n) for n=0..16

N. Lygeros & M. Mizony, Study of primality of terms of a_k(n)=(1+(sum from 1 to n-1)(a_k(i)^k))/(n-1)

D. Rusin, Law of small numbers

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

D. Zagier, Problems posed at the St Andrews Colloquium, 1996

D. Zagier, Solution: Day 5, problem 3

(PARI) A003504(n, s=2)=if(n-->0, for(k=1, n-1, s+=(s/k)^2); s/n, 1) \\ M. F. Hasler, Dec 12 2007

Cf. A005166, A005167, A108394, A115632, A116603 (asymptotic formula).

Sequence in context: A088938 A000617 A132183 this_sequence A003182 A134294 A130165

Adjacent sequences: A003501 A003502 A003503 this_sequence A003505 A003506 A003507

nonn,easy,nice

njas, R. K. Guy

a(0)..a(42) are integral, but from a(43) = 5.4093...*10^178485291567 onwards every term is nonintegral - H. W. Lenstra, Jr.

Corrected and extended by M. F. Hasler (maximilian.hasler(AT)gmail.com), Dec 12 2007