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A265849
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First differences of A006751.
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0
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10, 1100, 2000, 129000, 1112990000, 310198100000, 12900010100000, 1113122099909791900000, 31130009089198002000100000, 132082082098921801009009900000, 11131221131211000108018890978199979090100000, 31131122211299991892189900998999891000999919009909900000
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OFFSET
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1,1
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COMMENTS
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Note that A005150 has really different first differences characteristic because of its initial term that is 1.
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LINKS
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FORMULA
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a(n) mod 10^5 = 0, for n > 5.
a(2*n+2) - a(2*n) mod 10^6 = 0, for n > 3.
a(2*n+1) - a(2*n-1) mod 10^7 = 0, for n > 3.
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EXAMPLE
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MATHEMATICA
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f[n_, d_: 1] := NestList[Flatten[Reverse /@ Map[Function[k, Through[{First, Length}@ k]], Split@ #]] &, {d}, n - 1]; Differences@ Array[FromDigits@ f[#, 2][[#]] &, {13}] (* Michael De Vlieger, Jan 03 2016, after Zerinvary Lajos at A006751 *)
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PROG
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(PARI) dpt(n) = {vd = []; d = digits(n); nbd = 0; old = -1; for (k=1, #d, if (d[k] == old, nbd ++, if (old != -1, vd = concat(vd, nbd); vd = concat(vd, old); ); nbd = 1; ); old = d[k]; ); vd = concat(vd, nbd); vd = concat(vd, old); subst(Pol(vd), x, 10); }
lista(nn, x=2) = {v = vector(nn); v[1] = x; for (n=2, nn, nx = dpt(x); v[n] = nx; x = nx; ); vector(nn-1, n, v[n+1] - v[n]); } \\ 2nd param x can any value between 2 and 9 \\ Michel Marcus, Dec 16 2015
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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