A036066 The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.

1, 3, 1311, 2331, 331241, 14432231, 34433241, 54533231, 2544632221, 163534435221, 263544436231, 363554634231, 463554733221, 17364544733221, 37263554634231, 37363554734231, 37364544933221, 1937263554933221, 3927263544835231, 391827264534836231, 293827363544836231

Offset

0,2

Comments

After the 26th term the sequence goes into a cycle of 46 terms.

"Summarize" uses here method C = A244112: in order of decreasing digit value.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index to sequences related to say what you see

Formula

a(n+1) = A244112(concat(a(n),a(n-1))). - M. F. Hasler, Feb 25 2018

Maple

a:= proc(n) option remember; `if`(n<2, 2*n+1, (p-> parse(cat(seq((c->
     `if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
      add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1), a(n-2)]))))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 18 2022

Mathematica

a[0] = 1; a[1] = 3; a[n_] := a[n] = FromDigits @ Flatten @ Reverse @ Select[ Transpose @ { DigitCount[a[n-1]] + DigitCount[a[n-2]], Append[ Range[9], 0]}, #[[1]] > 0 &];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Dec 30 2017 *)

Prog

(PARI) {a=[1, 3]; for(n=1, 50, a=concat(a, A244112(eval(Str(a[n], a[n+1]))))); a} \\ M. F. Hasler, Feb 25 2018

Crossrefs

Cf. A036059.

Cf. A244112 (summarizing as used here: by decreasing digit value), A047842 (alternative summarizing method: by increasing digit value), A047843 (another method: don't omit missing digits between smallest and largest one).

Sequence in context: A129078 A174826 A122389 * A262516 A060307 A119111

Adjacent sequences: A036063 A036064 A036065 * A036067 A036068 A036069

Keyword

base,easy,nice,nonn

Author

Floor van Lamoen

Status

approved