A352740 - OEIS

%I #9 Apr 01 2022 09:03:48

%S 0,0,0,2,0,3,0,4,0,0,4,6,0,6,7,0,7,8,0,8,0,6,8,9,10,0,11,0,12,0,10,12,

%T 0,8,12,14,0,13,15,0,14,15,16,0,15,16,0,16,17,18,0,19,0,20,0,0,12,16,

%U 18,20,21,22,0,23,0,24,0,18,24,0,14,21,24,25,26

%N Irregular table T(n, k) read by rows; the n-th row contains, in ascending order, the numbers k < n such that for any base b >= 2, the sum of digits of n and k in base b are different.

%C A352671 gives row lengths.

%H Rémy Sigrist, <a href="/A352740/b352740.txt">Table of n, a(n) for n = 1..10302</a> (rows for n = 1..2000, flattened)

%H Rémy Sigrist, <a href="/A352671/a352671.png">Scatterplot of (x, y) such that x, y <= 1000 and for any base b >= 2, the sum of digits of x and y in base b are different</a>

%F T(n, 1) = 0.

%e irregular table begins:

%e      1:    [0]

%e      2:    [0]

%e      3:    [0, 2]

%e      4:    [0, 3]

%e      5:    [0, 4]

%e      6:    [0]

%e      7:    [0, 4, 6]

%e      8:    [0, 6, 7]

%e      9:    [0, 7, 8]

%e     10:    [0, 8]

%o (PARI) row(n) = { my (v=[]); for (k=0, n-1, my (ok=1); for (b=2, max(2, n+1), if (sumdigits(n, b)==sumdigits(k, b), ok=0; break)); if (ok, v=concat(v,k))); v }

%Y Cf. A216789, A352671 (row lengths).

%K nonn,base,tabf

%O 1,4

%A _Rémy Sigrist_, Mar 31 2022