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Search: id:A162467
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| A162467 |
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Numbers n such that the sum of all proper substrings of their decimal representation equals the reverse of n. |
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+0
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| 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 891, 941, 2931, 51070, 147970, 1330550, 1523870, 75914061, 30735249050, 32036090950, 90000000001, 575605978451, 922898423231, 21326410034240, 31829906273560, 93336794910541, 39470358768890551
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Here substrings are substrings of adjacent digits of length less than the number of digits of n, of which there are (d+2)*(d-1)/2=A000096(d-1), counted with multiplicity, where d=A055642(N).
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LINKS
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Ray Chandler, Table of n, a(n) for n=1..38
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FORMULA
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{n: A138953(n)=A004086(n)} - R. J. Mathar, Jul 06 2009
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EXAMPLE
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941 is in the list because 94 + 41 + 9 + 4 + 1 = 149.
51070 in in the list because 5107+1070+510+107+070+51+10+07+70+5+1+0+7+0=07015.
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CROSSREFS
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Cf. A125303 (substrings without multiplicity). - R. J. Mathar, Jul 06 2009
Sequence in context: A028440 A166511 A062237 this_sequence A033022 A031497 A020337
Adjacent sequences: A162464 A162465 A162466 this_sequence A162468 A162469 A162470
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KEYWORD
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nonn,base
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AUTHOR
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Claudio L Meller (claudiomeller(AT)gmail.com), Jul 04 2009
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EXTENSIONS
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Keyword base added, 10 to 90 and 147970 added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 06 2009
0 and a(16)-a(38) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 15 2009
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