A055481 Numbers k for which there exists some m such that k = Sum_{i=1..1+floor(log_10(k))} binomial(m, d_i), where d_i is the i-th digit of k.

1, 10, 18, 21, 72, 100, 101, 111, 134, 231, 246, 505, 682, 1000, 1010, 1100, 1122, 2210, 3103, 4006, 6008, 10000, 10001, 10012, 11101, 15453, 20101, 29358, 34698, 56576, 84304, 100000, 100010, 100011, 100100, 100101, 100110, 100303, 101000, 101001, 101010

Offset

1,2

Comments

Contains numbers of the form 10^k, k >= 0 so the sequence is infinite. - David A. Corneth, Oct 30 2018

Links

Giovanni Resta, Table of n, a(n) for n = 1..500

Example

3103 = C(22, 3) + C(22, 1) + C(22, 0) + C(22, 3).
C(k, 1) + C(k, 1) + C(k, 1) + C(k, 0) + C(k, 0) + C(k, 0) = 3k + 3 so all 6-digit numbers with 3 ones and 3 zeros are in the sequence. - David A. Corneth, Oct 30 2018

Mathematica

ok[n_] := Block[{d = IntegerDigits@n, k=1, v, x}, If[ Max@d <= 3, False =!= Reduce[ Total@ Binomial[x, d] == n && x>0, x, Integers], While[(v = Total@ Binomial[k, d]) < n, k++]; v == n]]; Select[ Range[10^5], ok] (* Giovanni Resta, Oct 30 2018 *)

Prog

(PARI) is(n) = my(d = digits(n)); for(i = 1, n, s = sum(j = 1, #d, binomial(i, d[j])); if(s >= n, return(s == n))) \\ David A. Corneth, Oct 30 2018

Crossrefs

Cf. A007088, A009994, A055482.

Sequence in context: A043767 A290002 A072992 * A213717 A333999 A245578

Adjacent sequences: A055478 A055479 A055480 * A055482 A055483 A055484

Keyword

base,nonn

Author

Erich Friedman, Jun 27 2000

Extensions

a(31)-a(41) from Giovanni Resta, Oct 30 2018

Status

approved