The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346430

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A346430

E.g.f.: 1 / (1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).
(history; published version)

#21 by Susanna Cuyler at Wed Aug 04 16:41:50 EDT 2021

STATUS

proposed

approved

#20 by Ilya Gutkovskiy at Wed Aug 04 09:52:28 EDT 2021

STATUS

editing

proposed

#19 by Ilya Gutkovskiy at Wed Aug 04 09:12:03 EDT 2021

CROSSREFS

Cf. A000040, A008578, A030017, A300632, A300662, A302194, A346791.

#18 by Ilya Gutkovskiy at Wed Aug 04 09:08:33 EDT 2021

NAME

allocated for Ilya Gutkovskiy

E.g.f.: 1 / (1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).

DATA

1, 1, 4, 21, 149, 1317, 13985, 173207, 2451807, 39043963, 690844441, 13446183857, 285500221447, 6567135007015, 162678487750465, 4317650962178897, 122234460353464081, 3676789159574231397, 117102826395968235853, 3936834192059910096205, 139316727760914366716635

OFFSET

0,3

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A008578(k) * a(n-k).

MATHEMATICA

nmax = 20; CoefficientList[Series[1/(1 - x - Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A000040, A008578, A030017, A300632, A300662, A302194.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Aug 04 2021

STATUS

approved

editing

#17 by Ilya Gutkovskiy at Wed Aug 04 09:08:33 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#16 by Bruno Berselli at Wed Aug 04 03:17:40 EDT 2021

STATUS

reviewed

approved

#15 by Hugo Pfoertner at Tue Aug 03 02:11:24 EDT 2021

STATUS

proposed

reviewed

#14 by Joerg Arndt at Tue Aug 03 02:07:05 EDT 2021

STATUS

editing

proposed

#13 by Joerg Arndt at Tue Aug 03 02:07:01 EDT 2021

NAME

Decimal expansion of Pi truncated to n places, thereafter the digits rearranged into nondecreasing order.

DATA

3, 13, 134, 1134, 11345, 113459, 1123459, 11234569, 112345569, 1123345569, 11233455569, 112334555689, 1123345556899, 11233455567899, 112334555678999, 1123334555678999, 11223334555678999, 112233334555678999, 1122333345556788999, 11223333445556788999

OFFSET

0,1

COMMENTS

It is still unknown whether Pi is a normal number. What is lim_{n->oo} floor(Pi*10^n)/a(n)?

LINKS

P. Trueb, <a href="https://arxiv.org/abs/1612.00489">Digit Statistics of the First 22.4 Trillion Decimal Digits of Pi</a>, arXiv:1612.00489 [math.NT], 2016.

FORMULA

a(n) = A004185(floor(Pi*10^n)).

CROSSREFS

Cf. A000796, A004185, A011545.

KEYWORD

nonn,base,changed

recycled

AUTHOR

Ctibor O. Zizka, Jul 17 2021

STATUS

proposed

editing

#12 by Alois P. Heinz at Mon Aug 02 10:29:55 EDT 2021

STATUS

editing

proposed

Discussion

Mon Aug 02

14:17

Hugo Pfoertner: Totally artificial. My vote is to reject and recycle.

14:47

Ctibor O. Zizka: Please do as you decide. Thank you.

15:20

Ctibor O. Zizka: + is the sequence which counts for ex. digit 3 in floor(Pi*10^n) : [1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,4,4,4,...]  interesting ?