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A101171
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a(n) divides the number formed by concatenating the sum of the digits of a(n) with a(n), by a factor not previously used.
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1
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1, 12, 15, 18, 25, 45, 75, 125, 1125, 1875, 5625, 16875, 140625, 1171875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| No more terms < 10^100. - David Wasserman (dwasserm(AT)earthlink.net), Mar 06 2008
All terms are of the form t=d*b^k where b=2 or 5 and d divides s = sum of digits of t. Let m be the decimal length of t. Assume that k>=140. Then we have m>=42 and thus log10(m)<m/25. Since d<10*m, we have m <= 1+log10(d*b^k) < 2+log10(m)+k*log10(b) < 2+(m/25)+0.7*k, implying that m < 2.1 + 0.73*k. On the other hand, b^k must divide s*10^m, implying that k < log10(s)/log10(2) + m < (1+log10(m))/log10(2) + m < 3.4 + 1.14*m < 5.8 + 0.84*k and hence k < 37. This contradiction proves that no term has k>=140, i.e., sequence is finite. - Max Alekseyev, May 08 2009
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EXAMPLE
| a(3) = 15 because the digit sum of 15 is 6 and 615/15 = 41. Any future number which divides its digit sum concatenated with itself by exactly 41 (such as 150, 225, 375, etc.) will be excluded.
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CROSSREFS
| Cf. A101170.
Sequence in context: A188766 A153047 A164782 * A120169 A115349 A196224
Adjacent sequences: A101168 A101169 A101170 * A101172 A101173 A101174
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KEYWORD
| base,nonn,full,fini
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AUTHOR
| Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 03 2004
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