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 A326746 #33 Oct 21 2019 21:44:08 %S A326746 0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,2,3,4,5,6,7,8,9,10,2,3,4,5,6, %T A326746 7,8,9,10,11,0,4,5,6,7,8,9,10,11,12,3,5,6,7,8,9,10,11,12,13,2,6,7,8,9, %U A326746 10,11,12,13,14,1,7,8,9,10,11,12,13,14,15,0,8,9,10,11,12,13,14,15,16,8,9,10 %N A326746 a(n) = (sum of digits of n) mod (sum of digits of n+1). %C A326746 For n > 100 the maximum value of a(n) increases by 1 a total of nine times for every order-of-magnitude increase of n; for n up to 10^10 the largest value of a(n) is 89. %C A326746 The frequency of occurrence for the values of a(n) for large values of n has an interesting distribution - it is a bell-shaped curve but with large increases for a(n) = 8, and a smaller increase for a(n) = 17. The value a(n) = 8 is likely the most common value as every time n increases by 100 the value of a(n) goes through ten smaller cycles, and 8 appears to be the only value that is present in all ten cycles. The reason a(n) = 17 also appears more often is not clear, although the distribution for n up to 10^10 also shows a slight increase in the number of occurrences for a(n) = 26, suggesting that a(n) values of the form a(n) = 8 + 9 * k, where k >= 0, occur more frequently than one would predicted from the surrounding bell-curve distribution. %C A326746 The sequence is unbounded because a(10^k-2) = 9*k-1 for k>0. - _Giovanni Resta_, Oct 19 2019 %H A326746 Scott R. Shannon, <a href="/A326746/b326746.txt">Table of n, a(n) for n = 0..19999</a> %H A326746 Scott R. Shannon, <a href="/A326746/a326746.png">Frequency distribution for a(n), where 0 <= a(n) <= 89, for n up to 10^10</a>. The large peak is a(n) = 8, which occurs 900169158 times. The smaller peak is a(n) = 17. There is also a small bump on the bell-curve at a(n) = 26; this may become a separate peak when n >> 10^10. The bell-curve maximum value is at a(n) = 44. %e A326746 a(1) = sum of digits of 1 mod sum of digits of 2 = 1 mod 2 = 1. %e A326746 a(9) = sum of digits of 9 mod sum of digits of 10 = 9 mod 1 = 0. %e A326746 a(38) = sum of digits of 38 mod sum of digits of 39 = 11 mod 12 = 11. %e A326746 a(39) = sum of digits of 39 mod sum of digits of 40 = 12 mod 4 = 0. %t A326746 sod[n_] := Plus @@ IntegerDigits@ n; a[n_] := Mod[sod[n], sod[n+1]]; Array[a, 100, 0] (* _Giovanni Resta_, Oct 19 2019 *) %o A326746 (PARI) a(n) = sumdigits(n) % sumdigits(n+1); \\ _Michel Marcus_, Oct 19 2019 %Y A326746 Cf. A070635, A180160. %K A326746 nonn,base,easy %O A326746 0,3 %A A326746 _Scott R. Shannon_, Oct 19 2019