A338827 For any number with decimal representation (d(1), d(2), ..., d(k)), the decimal representation of a(n) is (abs(d(1)-d(k)), abs(d(2)-d(k-1)), ..., abs(d(k)-d(1))).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 11, 22, 33, 44, 55, 66, 77, 88, 22, 11, 0, 11, 22, 33, 44, 55, 66, 77, 33, 22, 11, 0, 11, 22, 33, 44, 55, 66, 44, 33, 22, 11, 0, 11, 22, 33, 44, 55, 55, 44, 33, 22, 11, 0, 11, 22, 33, 44, 66, 55, 44, 33, 22, 11, 0, 11, 22

Offset: 0

Author

Rémy Sigrist, Nov 11 2020

Keywords

• nonn
• base
• look
• easy

Comments

Leading zeros are ignored.

All terms belong to A061917.

Examples

			For n = 1021:
- abs(1-1) = 0,
- abs(0-2) = 2,
- abs(2-0) = 2,
- abs(1-1) = 0,
- so a(1021) = 220.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002113, A004086, A056965, A061917, A175919 (binary analog), A330240, A338828 (ternary analog).

Programs

Maple

a:= n-> (l-> (h-> add(h[j]*10^(j-1), j=1..nops(h)))([seq(
    abs(l[i]-l[-i]), i=1..nops(l))]))(convert(n, base, 10)):
seq(a(n), n=0..70);  # Alois P. Heinz, Nov 12 2020

PARI

a(n, base=10) = my (d=digits(n, base)); fromdigits(abs(d-Vecrev(d)), base)

Formula

a(n) = 0 iff n is a palindrome (A002113).

a(n) = A330240(n, A004086(n)).