This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111072 #35 Aug 14 2024 08:34:28
%S A111072 0,1,4,10,10,15,16,24,30,35,40,46,54,55,60,60,66,69,70,70,70,71,74,80,
%T A111072 80,85,86,94,100,105,110,116,124,125,130,130,136,139,140,140,140,141,
%U A111072 144,150,150,155,156,164,170,175,180,186,194,195,200,200,206,209,210
%N A111072 Write the digit string 0123456789, repeated infinitely many times. Then, starting from the first "0" digit at the left end, move to the right by one digit (to the "1"), then two digits (to the "3"), then three digits (to the "6"), four digits ("0"), five digits ("5"), and so on. Partial sums of the digits thus reached are 0, 1, 4, 10, 10, 15, ...
%C A111072 The first differences 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, etc. are in A008954.
%D A111072 Giorgio Balzarotti and Paolo P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 62.
%H A111072 Michael De Vlieger, <a href="/A111072/b111072.txt">Table of n, a(n) for n = 0..10000</a>
%H A111072 J. Bokowski & N. J. A. Sloane, <a href="/A006248/a006248.pdf">Emails, June 1994</a>.
%F A111072 a(n+1) = a(n) + (a(n) - a(n-1) + (n+1) mod 10) mod 10, with a(0)=0, a(1)=1.
%F A111072 G.f.: x*(x^12+3*x^11+6*x^10+5*x^8+5*x^6+5*x^4+6*x^2+3*x+1) / (x^16 -x^15 -x^11 +x^10 +x^6 -x^5 -x +1). - _Alois P. Heinz_, Jan 23 2021
%e A111072 a(9) = 35 because a(8) - a(7) + (9 mod 10) = 30 - 24 + 9 = 15 and a(8) + (15 mod 10) = 30 + 5 = 35.
%e A111072 Jumping we move to the numbers 0, 1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0, 1, 3, 6, 0, 5, 1, 8, 6, etc. Summing the numbers we obtain 0, 0+1 = 1, 1+3 = 4, 4+6 = 10, 10+0 = 10, 10+5 = 16, etc.
%p A111072 a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+
%p A111072 [0,1,3,6,0,5,1,8,6,5,5,6,8,1,5,0,6,3,1,0,0]
%p A111072 [1+irem(n, 20)])
%p A111072 end:
%p A111072 seq(a(n), n=0..60); # _Alois P. Heinz_, Jan 23 2021
%t A111072 Fold[Append[#1, #1[[-1]] + Mod[(#1[[-1]] - #1[[-2]] + Mod[#2, 10]), 10]] &, {0, 1}, Range[2, 58]] (* _Michael De Vlieger_, Nov 05 2017 *)
%Y A111072 Cf. A008954.
%K A111072 nonn,base,easy
%O A111072 0,3
%A A111072 _Giorgio Balzarotti_ and _Paolo P. Lava_, Oct 10 2005