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A003508
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a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
(Formerly M0580)
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10
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1, 2, 3, 4, 7, 8, 11, 12, 18, 24, 30, 41, 42, 55, 72, 78, 97, 98, 108, 114, 139, 140, 155, 192, 198, 215, 264, 281, 282, 335, 408, 431, 432, 438, 517, 576, 582, 685, 828, 857, 858, 888, 931, 958, 1440, 1451, 1452, 1469, 1596, 1628, 1679, 1776, 1819, 1944
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| R. K. Guy reports, Apr 14 2005: In Math. Mag. 48 (1975) 301 one finds "C. W. Trigg, C. C. Oursler and R. Cormier & J. L. Selfridge have sent calculations on Problem 886 [Nov 1973] for which we had received only partial results [Jan 1975]. Cormier and Selfridge sent the following results: There appear to be five sequences beginning with integers less than 1000 which do not merge. These sequences were carried out to 10^8 or more." The five sequences are A003508, A105210-A105213.
This suggests that there may be infinitely many different (non-merging) sequences obtained by choosing different starting values.
All terms of these five sequences are distinct up to least 10^30. - T. D. Noe, Oct 19 2007
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REFERENCES
| Problem 886, Math. Mag., 48 (1975), 57-58.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..2000
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EXAMPLE
| a(6)=8, so a(7) = 8 + 1 + 2 = 11.
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MATHEMATICA
| a[1] = 1; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[ a[n - 1]]], # < a[n - 1] &]; Table[ a[n], {n, 54}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 13 2005)
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CROSSREFS
| Cf. A096460, A105221, A105233
Sequence in context: A065294 A188190 A026808 * A078662 A050048 A122456
Adjacent sequences: A003505 A003506 A003507 * A003509 A003510 A003511
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), May 09 2000
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