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A067254
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Numbers k such that the decimal encoding of the prime factorization of k (A067599) ends in k.
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1
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11, 8571, 11371, 190911, 12711811, 14713491, 19090911, 71119711, 12531135391, 15311195711, 112717566411, 158318548011, 518914376931, 7292811659931
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OFFSET
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1,1
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COMMENTS
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a(13) > 2*10^11. 518914376931, 7292811659931, 19090909090909090911 and prime repunits (A004022) are also terms. - Donovan Johnson, Dec 04 2012
a(15) > 10^13. If exponents equal to 1 are not represented (as in A080670), the corresponding sequence starts with 113113, 31373137, and 533517177839 = 853 * 3517 * 177839. - Giovanni Resta, Jun 26 2017
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LINKS
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EXAMPLE
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The prime factorization of 190911 is 3^1 * 7^1 * 9091^1 with decimal encoding 317190911, which ends in 190911. Hence 190911 is a term of the sequence.
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MATHEMATICA
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(*returns true if a ends with b, false o.w.*) f[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; e = StringLength[c]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[2]] == e, r = True]]; r]; (*gives the decimal encoding of the prime factorization of n*) g[n_] := FromDigits[Flatten[IntegerDigits[FactorInteger[n]]]]; Do[If[f[g[n], n], Print[n]], {n, 1, 10^6} ]
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PROG
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(PARI) {a067254(a, b) = local(n, v, k, j); for(n=max(2, a), b, v=factor(n); if(eval(concat(vector(matsize(v)[1], k, concat(vector(matsize(v)[2], j, Str(v[k, j]))))))%(10^length(Str(n)))==n, print1(n, ", ")))}
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CROSSREFS
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KEYWORD
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base,nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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