cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A047843 Describe n: give frequency of each digit, by increasing size; mention also missing digits between the smallest and largest one.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1011, 21, 1112, 110213, 11020314, 1102030415, 110203040516, 11020304050617, 1102030405060718, 110203040506070819, 100112, 1112, 22, 1213, 120314, 12030415, 1203040516
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Other methods to describe or summarize n are: A047842 (as here, but ignoring "missing" digits), A244112 (count digits in order of decreasing size, ignoring missing digits). - M. F. Hasler, Feb 25 2018

Examples

			131 contains two 1's, zero 2's and one 3, so a(131) = 210213.

Links

Crossrefs

Cf. A005151, A047841, A047842.

Programs

  • Mathematica
    a[n_] := Module[{T, f}, T = Tally[IntegerDigits[n]]; f[_] = 0; Do[f[t[[1]]] = t[[2]], {t, T}]; Table[{f[k], k}, {k, Min@T[[All, 1]], Max@T[[All, 1]]} ] // Flatten // FromDigits];
a /@ Range[0, 26] (* Jean-François Alcover, Jan 07 2020 *)
  • PARI
    A047843(n,S="")={if(n,for(d=vecmin(n=digits(n)),vecmax(n),S=Str(S,#select(t->t==d,n),d));eval(S),10)} \\ M. F. Hasler, Feb 25 2018

Extensions

More accurate title from M. F. Hasler, Feb 25 2018

A118628 "Say what you see".

Original entry on oeis.org

3, 13, 1113, 3113, 2123, 112213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314
Offset: 1

Views

Author

Parthasarathy Nambi, May 09 2006

Keywords

Examples

			3 = "one three" --> 13
13 = "one one, one three" --> 1113
1113 = "three ones, one three" --> 3113
3113 = "two ones, two threes" --> 2123

Links

Crossrefs

Cf. A005151.
Cf. A047842, A023989.

Programs

  • Haskell
    import Data.List (group, sort, transpose)
a118628 n = a118628_list !! (n-1)
a118628_list = 3 : f [3] :: [Integer] where
   f xs = (read $ concatMap show ys) : f (ys) where
          ys = concat $ transpose [map length zss, map head zss]
          zss = group $ sort xs
-- Reinhard Zumkeller, Jan 26 2014

Formula

a(n) = 21322314 for n > 12; a(n) = A005151(n) for n > 6. - Reinhard Zumkeller, Jan 26 2014
a(n) = A047842(a(n-1)). - Pontus von Brömssen, Jun 04 2023

A127354 Digit count of prime(n). The digit count numerically summarizes the frequency of digits 0 through 9 in that order when they occur in a number.

Original entry on oeis.org

12, 13, 15, 17, 21, 1113, 1117, 1119, 1213, 1219, 1113, 1317, 1114, 1314, 1417, 1315, 1519, 1116, 1617, 1117, 1317, 1719, 1318, 1819, 1719, 1021, 101113, 101117, 101119, 2113, 111217, 2113, 111317, 111319, 111419, 2115, 111517, 111316, 111617, 111317
Offset: 1

Views

Author

Lekraj Beedassy, Jan 11 2007

Keywords

Links

Crossrefs

Cf. A047842, A000040, A127355.

Programs

  • Haskell
    a127354 = a047842 . a000040  -- Reinhard Zumkeller, Apr 14 2014
  • Mathematica
    dc[n_] :=FromDigits@Flatten@Select[Table[{DigitCount[n, 10, k], k}, {k, 0, 9}], #[[1]] > 0 &];Table[dc[Prime[n]], {n, 40}] (* Ray Chandler, Jan 16 2007 *)

Formula

a(n) = A047842(A000040(n)).

A056967 Write what is described (putting a leading zero on numbers which have an odd number of digits).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 0, 111, 222, 333, 444, 555, 666, 777, 888, 999, 0, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888
Offset: 0

Views

Author

Henry Bottomley, Jul 20 2000

Keywords

Examples

			a(123130415)=3335 since it should be read as 01.23.13.04.15, i.e., zero 1's followed by two 3's followed by one 3 followed by zero 4's followed by one 5.

Crossrefs

Cf. A005150, A010785, A047842, A056966.

Programs

  • Python
    def A056967(n):
    s = str(n)
    s = '0'*(len(s)&1)+s
    return int('0'+''.join(s[i+1]*int(s[i])for i in range(0,len(s),2))) # Chai Wah Wu, Feb 12 2023

A097598 Describe n from right to left.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1011, 21, 1211, 1311, 1411, 1511, 1611, 1711, 1811, 1911, 1012, 1112, 22, 1312, 1412, 1512, 1612, 1712, 1812, 1912, 1013, 1113, 1213, 23, 1413, 1513, 1613, 1713, 1813, 1913, 1014, 1114, 1214, 1314, 24, 1514, 1614
Offset: 0

Views

Author

Odimar Fabeny, Aug 29 2004

Keywords

Crossrefs

Cf. A047842.

Extensions

More terms from Robert G. Wilson v, Aug 30 2004

A079664 a(n) = Sum_{i=1..n} LookAndSay(i).

Original entry on oeis.org

11, 23, 36, 50, 65, 81, 98, 116, 135, 1245, 1266, 2378, 3491, 4605, 5720, 6836, 7953, 9071, 10190, 11400, 12611, 12633, 13846, 15060, 16275, 17491, 18708, 19926, 21145, 22455, 23766, 25078, 25101, 26415, 27730, 29046, 30363, 31681, 33000, 34410
Offset: 1

Views

Author

Joseph L. Pe, Jan 26 2003

Keywords

Comments

A question related to this sequence: prove the convergence or divergence of the infinite series Sum_{i>=1} 1/LookAndSay(i). (Numerical experiments suggest that this diverges slowly.)

Examples

			a(2) = LookAndSay(1) + LookAndSay(2) = 11 (one "1") + 12 (one "2") = 23.

Crossrefs

Partial sums of A047842, n>=1.

A097846 Differences between A097598 and A045918.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -99, 0, 99, 198, 297, 396, 495, 594, 693, 792, -198, -99, 0, 99, 198, 297, 396, 495, 594, 693, -297
Offset: 0

Views

Author

Odimar Fabeny, Aug 31 2004

Keywords

Crossrefs

Cf. A045918, A047842, A097598, A097599, A097601.
Previous Showing 21-27 of 27 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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