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A301464 Sequence satisfies: 1 = Sum_{n>=1} n^(n-1) / a(n)^n, with a(1) = 2, by a greedy algorithm. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A085152 A264886 A287117

Adjacent sequences:  A301461 A301462 A301463 * A301465 A301466 A301467

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 26 2018

STATUS

approved

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Last modified January 21 19:07 EST 2021. Contains 340352 sequences. (Running on oeis4.)