The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A052382

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A052382

Numbers without 0 as a digit, a.k.a. zeroless numbers.
(history; published version)

#152 by Charles R Greathouse IV at Thu Sep 08 08:44:59 EDT 2022

PROG

(MAGMAMagma) [ n: n in [1..114] | not 0 in Intseq(n) ]; // Bruno Berselli, May 28 2011

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#151 by Alois P. Heinz at Sun Feb 16 15:55:02 EST 2020

STATUS

editing

approved

#150 by Alois P. Heinz at Sun Feb 16 15:54:30 EST 2020

COMMENTS

Integer n > 0 is encoded using bijective base-9 numeration, see Wikipedia link below. - Alois P. Heinz, Feb 16 2020

#149 by Alois P. Heinz at Sun Feb 16 15:48:41 EST 2020

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>

STATUS

approved

editing

#148 by M. F. Hasler at Tue Feb 04 14:29:07 EST 2020

STATUS

proposed

approved

#147 by Jon E. Schoenfield at Tue Jan 14 23:25:38 EST 2020

STATUS

editing

proposed

Discussion

Thu Jan 16

23:40

M. F. Hasler: BS: It's fine with me. ___
JJ: when you say "program with more than one line is overkill", do you mean we should delete the lengthy Smalltalk programs?

Mon Jan 27

02:03

Joerg Arndt: delete the lengthy Smalltalk programs?  No, but just out of respect for the author of those programs.

#146 by Jon E. Schoenfield at Tue Jan 14 23:25:31 EST 2020

PROG

\\ See OEIS wiki Wiki page (cf. LINKS) for more programs. - M. F. Hasler, Jan 11 2020

STATUS

proposed

editing

#145 by M. F. Hasler at Mon Jan 13 22:11:44 EST 2020

STATUS

editing

proposed

Discussion

Tue Jan 14

03:08

Bernard Schott: Yes, MFH, you're right. Formula section is overcrowded, but there is no problem to delete my last comment, if it is redundant.

#144 by M. F. Hasler at Mon Jan 13 22:07:02 EST 2020

FORMULA

Sum_{n>=1} 1/a(n) = 23.1034479..., the = A082839. This so-called Kempner series converges very slowly. For the calculation of the sum, it is helpful to use the following fraction of partial sums, which converges rapidly:

Lim_lim_{n->infinity} (Sum_{k=p(n)..p(n+1)-1} 1/a(k)) / (Sum_{k=p(n-1)..p(n)-1} 1/a(k)) = 9/10, where p(n) = (9^n-1)/8, n > 1.

EXAMPLE

From _For k >= 0, a(10^k) = (1, 11, 121, 1331, 14641, 162151, 1783661, 19731371, ...) = A325203(k). - _Hieronymus Fischer_, May 30 2012, and Jun 06 2012, and May 28 2014; edited by M. F. Hasler, Jan 13 2020: (Start)

a(10^k) = (1, 11, 121, 1331, 14641, 162151, ...) = A325203(k), for k >= 0. (End)

PROG

next_A052382(n, d=digits(n+=1))={for(i=1, #d, d[i]|| return(n-n%(d=10^(#d-i+1))+d\9)); n} \\ least a(k) > n, useful to compute {N <= a(k) <= M}, e.g Used in A038618.:

( {A052382_vec(n, M=1)=M--; vector(n, i, M=next_A052382(M))} )(99) \\ n terms >= M

\\ _See OEIS wiki page (cf. LINKS) for more programs. - _M. F. Hasler_, Jan 11 2020

STATUS

proposed

editing

Discussion

Mon Jan 13

22:11

M. F. Hasler: The COMMENT from B.Schott (Feb 23 2019) is the same as the last FORMULA from H.Fischer (Feb 20 2019) [I just added name & A-number there]. If the entry wasn't that much overcrowded, we wouldn't need the same information twice....

#143 by M. F. Hasler at Mon Jan 13 21:41:23 EST 2020

STATUS

editing

proposed