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Search: id:A092096
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| A092096 |
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Summands (or semi-duals) of Smarandacheials S(n,k) for k=5. |
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+0
2
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| 11, 12, 20, 20, 30, 31, 32, 45, 45, 60, 61, 62, 80, 80, 100, 101, 102, 125, 125, 150, 151, 152, 180, 180, 210, 211, 212, 245, 245, 280, 281, 282, 320, 320, 360, 361, 362, 405, 405, 450, 451, 452, 500, 500, 550, 551, 552, 605, 605, 660, 661, 662, 720, 720, 780
(list; graph; listen)
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OFFSET
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6,1
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COMMENT
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More generally: Let n>k>=1 be two integers and m>=0 another integer. Then the Generalized Back and Forth Summand is defined as: S_abs(n, m, k) = Sigma_{i=0,1,2,..., floor[(n+m)/k]}(abs(n-k*i)).
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REFERENCES
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J. Dezert, editor, Smarandacheials, Mathematics Magazine, Aurora, Canada, No. 4/2004.
F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.
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LINKS
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J. Dezert, Smarandacheials
J. Dezert, Smarandacheials, "Mathematics Magazine", Canada
F. Smarandache, Summants
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FORMULA
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S_abs(n, 5) = Sigma_{i=0, 1, 2, ...}_{0<abs(n-5i)<=n}(abs(n-5i)) = n+abs(n-5)+abs(n-10)+ ...
a(n) = sum_{i=0,1,2,..; n-k*i>= -n} |n-k*i| at k=5. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 01 2008
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EXAMPLE
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S_abs(11, 5) = 11+abs(11-5)+abs(11-10)+abs(11-15)+abs(11-20) = 11+6+1+4+9 = 31.
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MAPLE
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S := proc(n, k) local a, i ; a :=0 ; i := 0 ; while n-k*i >= -n do a := a+abs(n-k*i) ; i := i+1 ; od: RETURN(a) ; end: k := 5: seq(S(n, k), n=k+1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 01 2008
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CROSSREFS
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Cf. A001044, A092396, A092397, A092398, A092399, A092971, A092972, A092973, A092974.
Sequence in context: A046465 A134926 A105744 this_sequence A057303 A121979 A109372
Adjacent sequences: A092093 A092094 A092095 this_sequence A092097 A092098 A092099
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KEYWORD
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nonn
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AUTHOR
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Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 01 2008
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