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A213630
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a(t_1 t_2...t_n) = (t_1 + t_2)*t_1 t_2 + ... + (t_n-1 + t_n)*t_n-1 t_n.
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1
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1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 160, 205, 252, 301, 352, 405, 460, 517, 576, 637, 250, 306, 364, 424, 486, 550, 616
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OFFSET
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1,2
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COMMENTS
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Differs from A057147 first at n=100.
a(n)/n = {1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, ...}. - Alexander R. Povolotsky, Jun 19 2012
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LINKS
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FORMULA
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Let t_1t_2...t_n be a natural number.
a(t_1t_2...t_n) = (t_1 + t_2)*t_1t_2 + ... + (t_n-1 + t_n)*t_n-1t_n, if n even.
If n is odd, t_1 t_2...t_n <- 0t_1t_2...t_n and do a(0t_1 t_2...t_n).
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EXAMPLE
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a(123456) = (1+2)*12 + (3+4)*34 + (5+6)*56 = 890.
a(890) = (0+8)*08 + (9+0)*90 = 874.
a(15) = (1+5)*15 = 90.
a(7) = (0+7)*07 = 49.
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MAPLE
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read("transforms"):
local dgs, a, i ;
if n < 10 then
n^2;
else
dgs := convert(n, base, 10) ;
a := 0 ;
for i from 2 to nops(dgs) do
a := a+(op(i-1, dgs)+op(i, dgs))*digcat2(op(i, dgs), op(i-1, dgs)) ;
end do:
a;
end if;
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MATHEMATICA
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num[n_] := Module[{d = IntegerDigits[n], d2}, If[OddQ[Length[d]], d = Prepend[d, 0]]; d2 = Partition[d, 2]; Sum[(d2[[i, 1]] + d2[[i, 2]])*(10*d2[[i, 1]] + d2[[i, 2]]), {i, Length[d2]}]]; Table[num[n], {n, 100}] (* T. D. Noe, Jun 19 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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