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 A173525 a(n) = 1 + A053824(n-1), where A053824 = sum of digits in base 5. 8
 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also: a(n) = A053824(5^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053824. (See the comment by M. F. Hasler for the proof.) This means: if A053824 is regarded as a triangle then the rows converge to this sequence. See conjecture in the entry A000120, and the case of base 2 in A063787. From R. J. Mathar, Dec 09 2010: (Start) In base b=5, A053824 starts counting up from 1 each time the index wraps around a power of b: A053824(b^k)=1. Obvious recurrences are A053824(m*b^k+i) = m+A053824(i), 1 <= m < b-1, 0 <= i < b^(k-1). So A053824 can be decomposed into a triangle T(k,n) = A053824(b^k+n-1), assuming that column indices start at n=1; row lengths are (b-1)*b^k. There is a self-similarity in these sequences; a sawtooth structure of periodicity b is added algebraically on top of a sawtooth structure of periodicity b^2, on top of a periodicity b^3 etc. This leads to some "fake" finitely periodic substructures in the early parts of each row of T(.,.): often, but not always, a(n+b)=1+a(n). Often, but not always, a(n+b^2)=1+a(n) etc. The common part of the rows T(.,.) grows with the power of b as shown in the recurrence above, and defines a(n) in the limit of large row indices k. (End) The two definitions agree because the first 5^r terms in each row correspond to numbers 5^r, 5^r+1,...,5^r+(5^r-1), which are written in base 5 as a leading 1 plus the digits of 0,...,5^r-1. - M. F. Hasler, Dec 09 2010 From Omar E. Pol, Dec 10 2010: (Start) In the scatter plots of these sequences, the basic structure is an element with b^2 points, where b is the associated base. (Scatter plots are created with the "graph" button of a sequence.) Sketches of these structures look as follows, the horizontal axis a squeezed version of the index n, b consecutive points packed vertically, and the vertical axis a(n): ........................................................ ................................................ * ..... ............................................... ** ..... ..................................... * ...... *** ..... .................................... ** ..... **** ..... .......................... * ...... *** .... ***** ..... ......................... ** ..... **** ... ****** ..... ............... * ...... *** .... ***** ... ***** ...... .............. ** ..... **** .... **** .... **** ....... .... * ...... *** ..... *** ..... *** ..... *** ........ ... ** ...... ** ...... ** ...... ** ...... ** ......... ... * ....... * ....... * ....... * ....... * .......... ........................................................ ... b=2 ..... b=3 ..... b=4 ..... b=5 ..... b=6 ........ . A000120 . A053735 . A053737 . A053824 . A053827 ...... . A063787 . A173523 . A173524 . A173525 . A173526 ...... ........................................................ ............................................. * ........ ............................................ ** ........ ........................... * ............. *** ........ .......................... ** ............ **** ........ ........... *............ *** ........... ***** ........ .......... ** .......... **** .......... ****** ........ ......... ***.......... ***** ......... ******* ........ ........ **** ........ ****** ........ ******** ........ ....... ***** ....... ******* ....... ********* ........ ...... ****** ...... ******** ....... ******** ......... ..... ******* ...... ******* ........ ******* .......... ..... ****** ....... ****** ......... ****** ........... ..... ***** ........ ***** .......... ***** ............ ..... **** ......... **** ........... **** ............. ..... *** .......... *** ............ *** .............. ..... ** ........... ** ............. ** ............... ..... * ............ * .............. * ................ ........................................................ ..... b=7 .......... b=8 ............ b=9 .............. ... A053828 ...... A053829 ........ A053830 ............ ... A173527 ...... A173528 ........ A173529 ............(End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..3126=5^5+1 Robert Walker, Self Similar Sloth Canon Number Sequences FORMULA a(n) = A053824(5^k + n - 1) where k >= ceiling(log_5(n/4)). - R. J. Mathar, Dec 09 2010 MAPLE A053825 := proc(n) add(d, d=convert(n, base, 5)) ; end proc: A173525 := proc(n) local b, k; b := 5 ; if n < b then n; else k := n/(b-1);   k := ceil(log(k)/log(b)) ; A053825(b^k+n-1) ; end if; end proc: seq(A173525(n), n=1..100) ; MATHEMATICA Total[IntegerDigits[#, 5]]+1&/@Range[0, 100] (* Harvey P. Dale, Jun 14 2015 *) PROG (PARI) A173525(n)={ my(s=1); n--; until(!n\=5, s+=n%5); s } \\ M. F. Hasler, Dec 09 2010 (PARI) A173525(n)={ my(s=1+(n=divrem(n-1, 5))[2]); while((n=divrem(n[1], 5))[1], s+=n[2]); s+n[2] } \\ M. F. Hasler, Dec 09 2010 (Haskell) a173525 = (+ 1) . a053824 . (subtract 1) -- Reinhard Zumkeller, Jan 31 2014 CROSSREFS Cf. A000120, A053824, A063787, A173523, A173524, A173526, A173527, A173528, A173529. Sequence in context: A212176 A070671 A119281 * A070772 A094937 A215089 Adjacent sequences:  A173522 A173523 A173524 * A173526 A173527 A173528 KEYWORD nonn,base,look AUTHOR Omar E. Pol, Feb 20 2010 EXTENSIONS More terms from Vincenzo Librandi, Aug 02 2010 STATUS approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)