A007651 Describe the previous term! (method B - initial term is 1).

1, 11, 12, 1121, 122111, 112213, 12221131, 1123123111, 12213111213113, 11221131132111311231, 12221231123121133112213111, 1123112131122131112112321222113113, 1221311221113112221131132112213121112312311231

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy
• nice

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			The term after 1121 is obtained by saying "1 twice, 2 once, 1 once", which gives 122111.
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..25

Crossrefs

Cf. A005150, A022470, A022499, A022500-A022505.

Programs

Haskell

a007651 = foldl1 (\v d -> 10 * v + d) . map toInteger . a220424_row
-- Reinhard Zumkeller, Dec 15 2012

Mathematica

RunLengthEncode[ x_List ] := (Through[ {First, Length}[ #1 ] ] &) /@ Split[ x ]; LookAndSay[ n_, d_:1 ] := NestList[ Flatten[ Reverse /@ RunLengthEncode[ # ] ] &, {d}, n - 1 ]; F[ n_ ] := LookAndSay[ n, 1 ][ [ n ] ]; Table[ FromDigits[ Reverse[ F[ n ] ] ], {n, 1, 15} ]
a[1] = 1; a[n_] := a[n] = FromDigits[Flatten[{First[#], Length[#]}&/@Split[IntegerDigits[a[n-1]]]]]; Map[a, Range[25]] (* Peter J. C. Moses, Mar 22 2013 *)

Python

from itertools import accumulate, groupby, repeat
def summarize(n, _): return int("".join(k+str(len(list(g))) for k, g in groupby(str(n))))
def aupto(terms): return list(accumulate(repeat(1, terms), summarize))
print(aupto(13)) # Michael S. Branicky, Sep 18 2022

Formula

a(n) = Sum_{k=1..A005341(n)} A220424(n,k)*10^(A005341(n)-k). - Reinhard Zumkeller, Dec 15 2012