A071762 Leftmost 1 is converted to a 2, which then propagates one step at a time until it is rightmost; then it changes to a pair of 1's and the process repeats.

0, 1, 2, 11, 21, 12, 111, 211, 121, 112, 1111, 2111, 1211, 1121, 1112, 11111, 21111, 12111, 11211, 11121, 11112, 111111, 211111, 121111, 112111, 111211, 111121, 111112, 1111111, 2111111, 1211111, 1121111, 1112111, 1111211, 1111121, 1111112, 11111111, 21111111

Offset

0,3

Comments

Arises in analysis of Bulgarian solitaire.

From J.N. Cressey, Apr 24 2026: (Start)

To construct a(n) for n > 0: repeat the digit 1 A003056(n) times. Let r = A002262(n). If r > 0, replace the digit at position r, 1-indexed from the left, with the digit 2.

The run lengths of 1's from either end in the decimal representation are given by: A128138(n) from the left end, for n >= 1; and A025581(n) from the right end. (End)

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = A002275(A003056(n)) + (1-A010054(n))*10^A025581(n). - J.N. Cressey, Apr 19 2026

Mathematica

f1[{a_, b_}]:={a, NestList[FromDigits[RotateRight[IntegerDigits[#]]]&, b, IntegerLength[ b]-1]}; Join[{0}, f1/@Table[{FromDigits[PadRight[{}, n, 1]], FromDigits[ PadRight[{2}, n, 1]]}, {n, 7}]//Flatten] (* Harvey P. Dale, May 15 2018 *)

Prog

(Python)
from math import comb, isqrt
def a(n):
    L, i = (isqrt(1+8*n)-1)//2, n-comb((1+isqrt(8+8*n))//2, 2) # A003056(n), A002262(n)
    return 10**L//9 + int(i > 0)*10**(L-i)
print([a(n) for n in range(38)]) # Michael S. Branicky, Apr 24 2026

Crossrefs

Cf. A071761.

Cf. A003056, A002262, A002275, A010054, A025581, A057944, A128138.

Sequence in context: A094629 A336034 A081242 * A288945 A343450 A245500

Adjacent sequences: A071759 A071760 A071761 * A071763 A071764 A071765

Keyword

nonn,easy

Author

Allan C. Wechsler, Jun 07 2002

Extensions

More terms from Sascha Kurz, Jan 28 2003

Status

approved