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Search: id:A130877
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| A130877 |
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Numbers n such that n = Sum_digits[k*(n+k)] for some k>=0. |
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+0
2
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| 0, 5, 9, 14, 18, 23, 27, 32, 36, 41, 45, 50, 54, 59, 63, 68, 72, 77, 81, 86, 90, 95, 99, 104, 108, 113, 117, 122, 126, 131, 135, 140, 144, 149, 153, 158, 162, 167, 171, 176, 180, 185, 189, 194, 198, 203, 207, 212, 216, 221, 225, 230, 234, 239, 243, 248, 252, 257
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The first differences are 2-periodic: 5, 4, 5, 4, etc. The minimum numbers k associated to the first elements of the sequence are (n,k): (0,0), (5,2), (9,3), (14,5), (18,15), (23,44), (27,42), (32,119), etc.
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FORMULA
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a(n)=9/2*(n+1)-4+Sum{j=0..n}{(-1)^j/2}
O.g.f.: x^2(5+4x)/((1+x)(1-x)^2). a(n)=9(n-1)/2+(1+(-1)^n)/4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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EXAMPLE
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n = 41 -> k = 797 -> 797*(41+797)=797*838=667886 -> 6+6+7+8+8+6 = 41
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MAPLE
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P:=proc(n) local i, j, k, w; for i from 0 by 1 to n do for j from 0 by 1 to 100*n do w:=0; k:=j*(i+j); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if w=i then print(i); break; fi; od; od; end: P(100000);
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CROSSREFS
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Sequence in context: A101116 A030772 A084597 this_sequence A140490 A079509 A074375
Adjacent sequences: A130874 A130875 A130876 this_sequence A130878 A130879 A130880
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KEYWORD
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nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Jul 25 2007
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