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A243994 Consider a decimal number of k>=2 digits x = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1) and the transform T(x)-> (d_(k)+d_(k-1) mod 10)*10^(k-1) + (d_(k-1)+d_(k-2) mod 10)*10^(k-2) + … + (d_(2)+d_(1) mod 10)*10 + (d_(1)+d(k) mod 10). Sequence lists the numbers x such that T(x)=0. 3

%I #18 Jul 07 2014 00:29:40

%S 19,28,37,46,55,64,73,82,91,191,282,373,464,555,646,737,828,919,1919,

%T 2828,3737,4646,5555,6464,7373,8282,9191,19191,28282,37373,46464,

%U 55555,64646,73737,82828,91919,191919,282828,373737,464646,555555,646464,737373,828282

%N Consider a decimal number of k>=2 digits x = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1) and the transform T(x)-> (d_(k)+d_(k-1) mod 10)*10^(k-1) + (d_(k-1)+d_(k-2) mod 10)*10^(k-2) + … + (d_(2)+d_(1) mod 10)*10 + (d_(1)+d(k) mod 10). Sequence lists the numbers x such that T(x)=0.

%F Empirical g.f.: -x*(90*x^17 -100*x^16 +90*x^15 -100*x^14 +90*x^13 -100*x^12 +90*x^11 -100*x^10 +90*x^9 -19*x^8 +10*x^7 -19*x^6 +10*x^5 -19*x^4 +10*x^3 -19*x^2 +10*x -19) / ((x -1)*(x^2 -x +1)*(x^6 -x^3 +1)*(10*x^9 -1)). - _Colin Barker_, Jun 17 2014

%e For 19 we have (1+9) mod 10 = 10 mod 10 = 0 and (9+1) mod 10 = 10 mod 10 = 0.

%e All the terms are created by concatenating the elements of the following sets of digits only with themselves: {1,9}, {2,8}, {3,7}, {4,6}, {5}.

%p P:=proc(q) local a,b,c,j,n;

%p for n from 10 to q do a:=[]; b:=n; while b>0 do a:=[b mod 10,op(a)];

%p b:=trunc(b/10); od; b:=0; c:=0; b:=(c[nops(c)]+c[1]) mod 10;

%p for j from 1 to nops(a)-1 do c:=c*10+((a[j]+a[j+1]) mod 10); od; c:=c*10+b;

%p if c=0 then print(n); fi; od; end: P(10^10);

%Y Cf. A243993.

%K nonn,easy,base

%O 1,1

%A _Paolo P. Lava_, Jun 17 2014

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Last modified July 22 00:58 EDT 2024. Contains 374478 sequences. (Running on oeis4.)