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A055481
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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.
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2
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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
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OFFSET
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1,2
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COMMENTS
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Contains numbers of the form 10^k, k >= 0 so the sequence is infinite. - David A. Corneth, Oct 30 2018
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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