A301464 Sequence satisfies: 1 = Sum_{n>=1} n^(n-1) / a(n)^n, with a(1) = 2, by a greedy algorithm.

2, 3, 4, 5, 8, 9, 15, 17, 21, 28, 33, 38, 50, 61, 72, 78, 86, 91, 110, 123, 141, 161, 178, 187, 214, 230, 239, 253, 278, 291, 302, 314, 338, 352, 398, 410, 422, 448, 462, 474, 492, 548, 591, 609, 661, 684, 716, 757, 801, 835, 856, 897, 915, 969, 1005, 1061, 1085, 1108, 1153, 1206, 1249, 1286, 1315, 1338, 1386, 1412, 1552, 1585, 1615, 1645, 1669, 1731, 1771, 1798, 1830, 1873, 1902, 1972, 2023, 2051

Offset

1,1

Comments

It appears that limit a(n)/n^2 exists and is near exp(-1).

Links

Paul D. Hanna, Table of n, a(n) for n = 1..3000

Example

1 = 1/2 + 2/3^2 + 3^2/4^3 + 4^3/5^4 + 5^4/8^5 + 6^5/9^6 + 7^6/15^7 + 8^7/17^8 + 9^8/21^9 + 10^9/28^10 + 11^10/33^11 + 12^11/38^12 + 13^12/50^13 + 14^13/61^14 + 15^14/72^15 + 16^15/78^16 + 17^16/86^17 + 18^17/91^18 + 19^18/110^19 + 20^19/123^20 + 21^20/141^21 + 22^21/161^22 + 23^22/178^23 + 24^23/187^24 + 25^24/214^25 + 26^25/230^26 + 27^26/239^27 + ... + n^(n-1)/a(n)^n + ...

Prog

(PARI) /* Must use appropriate precision to obtain N terms: */ N=100;
A=[2, 3]; for(i=3, N, A=concat(A, ceil((1/(1 - sum(n=1, #A, n^(n-1)/A[n]^n * 1.))*(#A+1)^(#A) )^(1/(#A+1))) ) ); A

Crossrefs

Sequence in context: A240080 A194714 A054168 * A354829 A085152 A264886

Adjacent sequences: A301461 A301462 A301463 * A301465 A301466 A301467

Keyword

nonn

Author

Paul D. Hanna, Mar 26 2018

Status

approved