A331163 a(n) is the number of occurrences of the most frequently seen difference between adjacent digits in the concatenation of a(0) to a(n-1), with a(0) = 0, a(1) = 0.

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 12, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 22, 23, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 30, 31, 31, 31, 31, 31

Offset

0,5

Comments

In the first 10 million terms the most frequently seen digit difference is 1, which leads other digit difference counts for 2589052 terms. The least seen is 9, which only holds the lead for 990 terms and does not become the most frequently seen digit difference until a(23521), after a run of 1228 consecutive terms of 9090. The longest series of unchanging terms begins at a(7727945) = 7040480 which begins a run of 94553 consecutive terms of 7040480.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

a(2) = 1 as the concatenation of a(0) and a(1) = '00', and the only adjacent digit difference in '00' is 0, and that difference has occurred one time.
a(3) = 1 as the adjacent digit differences in '001' are 0 and 1, both of which have occurred one time.
a(4) = 2 as '0011' contains two pairs of adjacent digits which differ by 0.
a(22) = 12 as '001122334455667788991010' contains twelve pairs of adjacent digits which differ by 1.

Maple

DC:= [0]: last:= 0:
Res:= 0, 0:
Ct:= Array(0..9):
Ct[0]:= 1:
for n from 2 to 100 do
  v:= max(Ct);
  Res:= Res, v;
  L:= [last, op(ListTools:-Reverse(convert(v, base, 10)))];
  DL:= map(abs, L[2..-1]-L[1..-2]);
  last:= L[-1];
  for i from 1 to nops(DL) do
    Ct[DL[i]]:= Ct[DL[i]]+1
  od;
od:
Res; # Robert Israel, Jan 16 2020

Crossrefs

Cf. A040115.

Sequence in context: A327036 A358854 A330015 * A157271 A025162 A330027

Adjacent sequences: A331160 A331161 A331162 * A331164 A331165 A331166

Keyword

nonn,base

Author

Scott R. Shannon, Jan 11 2020

Status

approved