A265849 First differences of A006751.

10, 1100, 2000, 129000, 1112990000, 310198100000, 12900010100000, 1113122099909791900000, 31130009089198002000100000, 132082082098921801009009900000, 11131221131211000108018890978199979090100000, 31131122211299991892189900998999891000999919009909900000

Offset: 1

Author

Altug Alkan, Dec 16 2015

Keywords

• nonn
• base
• easy

Comments

Also first differences of A006715, A001140, A001141, A001143, A001145, A001151, A001154. - Michel Marcus, Dec 16 2015

Note that A005150 has really different first differences characteristic because of its initial term that is 1.

Examples

			a(1) = A006751(2) - A006751(1) = 12 - 2 = 10.
a(2) = A006751(3) - A006751(2) = 1112 - 12 = 1100.
		

Crossrefs

Cf. A006751, A006715, A001140, A001141, A001143, A001145, A001151, A001154.

Programs

Mathematica

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 *)

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

Formula

a(n) = A006751(n+1) - A006751(n).

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.