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 A363683 #5 Jun 17 2023 14:22:53
%S A363683 1,4,4,9,1,9,2,17,17,2,3,7,1,7,3,4,5,8,8,5,4,5,4,9,1,9,4,5,8,2,3,11,
%T A363683 11,3,2,8,16,5,11,6,1,6,11,5,16,1,17,7,4,9,9,4,7,17,1,1,4,17,10,6,1,6,
%U A363683 10,17,4,1,1,4,9,14,5,15,15,5,14,9,4,1
%N A363683 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the least e > 0 such that n^e and k^e have the same initial digit, or -1 if no such e exists.
%C A363683 Conjecture: all terms are positive.
%H A363683 Rémy Sigrist, <a href="/A363683/a363683.png">Colored representation of the table for n, k <= 1200</a>
%F A363683 A(n, k) = A(k, n).
%F A363683 A(10*n, k) = A(n, k).
%F A363683 A(n, n) = 1.
%F A363683 A(n, 1) = A098174(n).
%e A363683 Array A(n, k) begins:
%e A363683 n\k | 1 2 3 4 5 6 7 8 9 10 11 12
%e A363683 ----+-----------------------------------------------
%e A363683 1 | 1 4 9 2 3 4 5 8 16 1 1 1
%e A363683 2 | 4 1 17 7 5 4 2 5 17 4 4 9
%e A363683 3 | 9 17 1 8 9 3 11 7 17 9 16 5
%e A363683 4 | 2 7 8 1 11 6 4 10 14 2 2 2
%e A363683 5 | 3 5 9 11 1 9 6 5 4 3 3 3
%e A363683 6 | 4 4 3 6 9 1 15 7 11 4 4 10
%e A363683 7 | 5 2 11 4 6 15 1 17 18 5 5 4
%e A363683 8 | 8 5 7 10 5 7 17 1 18 8 28 6
%e A363683 9 | 16 17 17 14 4 11 18 18 1 16 23 8
%e A363683 10 | 1 4 9 2 3 4 5 8 16 1 1 1
%e A363683 11 | 1 4 16 2 3 4 5 28 23 1 1 1
%e A363683 12 | 1 9 5 2 3 10 4 6 8 1 1 1
%o A363683 (PARI) A(n,k) = { for (e = 1, oo, if (digits(n^e)[1]==digits(k^e)[1], return (e));); }
%Y A363683 Cf. A000030, A073601, A088995, A098174, A359698.
%K A363683 nonn,base,tabl
%O A363683 1,2
%A A363683 _Rémy Sigrist_, Jun 15 2023