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.

19, 28, 37, 46, 55, 64, 73, 82, 91, 191, 282, 373, 464, 555, 646, 737, 828, 919, 1919, 2828, 3737, 4646, 5555, 6464, 7373, 8282, 9191, 19191, 28282, 37373, 46464, 55555, 64646, 73737, 82828, 91919, 191919, 282828, 373737, 464646, 555555, 646464, 737373, 828282

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Formula

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

Example

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

Maple

P:=proc(q) local a, b, c, j, n;
for n from 10 to q do a:=[]; b:=n; while b>0 do a:=[b mod 10, op(a)];
b:=trunc(b/10); od; b:=0; c:=0; b:=(c[nops(c)]+c[1]) mod 10;
for j from 1 to nops(a)-1 do c:=c*10+((a[j]+a[j+1]) mod 10); od; c:=c*10+b;
if c=0 then print(n); fi; od; end: P(10^10);

Crossrefs

Cf. A243993.

Sequence in context: A094677 A052224 A179955 * A083678 A279771 A257043

Adjacent sequences: A243991 A243992 A243993 * A243995 A243996 A243997

Keyword

nonn,easy,base

Author

Paolo P. Lava, Jun 17 2014

Status

approved