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%I #16 Oct 10 2024 08:54:22
%S 1,3,5,4,11,10,16,25,31,41,-1,57,56,75,73,80,-1,108,110,142,112,149,
%T 148,155,154,168,194,203,221,238,-1,271,-1,-1,308,-1,360,414,416,437,
%U -1,-1,484,-1,-1,529,-1,660,-1,740,944,760,869,916,984,-1,1010,1016,1020,-1,1032,-1,1193,1219,1160,1329,1264,1331,1200,1426,1303,1350,1369,1473,1543
%N Irregular table read by rows: row(n) lists the positive numbers k in each base n such that the sum of its digits when written in all bases 2 to n equals k, or -1 if no such number exists.
%C The first base with two numbers is 3, the first base with three numbers is 14, the first base with four numbers is 88, and the first base with five numbers is 440. It is unknown if a base can contain an arbitrary number of such values.
%C See A376816 for the smallest number in each base n.
%H Scott R. Shannon, <a href="/A376817/b376817.txt">Table of n, a(n) for n = 2..720</a>
%H Scott R. Shannon, <a href="/A376817/a376817.txt">Unflattened table for n = 2..500</a>
%e row(4) = 4, 11; as 4 = 100_2 = 11_3 = 10_4, and the sum of all these digits is 1 + 0 + 0 + 1 + 1 + 1 + 0 = 4, and 11 = 1011_2 = 102_3 = 23_4, and the sum of all these digits is 1 + 0 + 1 + 1 + 1 + 0 + 2 + 2 + 3 = 11.
%e The table begins:
%e 1;
%e 3, 5;
%e 4, 11;
%e 10;
%e 16;
%e 25, 31;
%e 41;
%e -1;
%e 57;
%e 56, 75;
%e 73, 80;
%e -1;
%e 108, 110, 142;
%e 112, 149;
%e 148, 155;
%e 154, 168, 194;
%e 203;
%e 221, 238;
%e ...
%Y Cf. A376816, A004209, A007953.
%K sign,base,tabf
%O 2,2
%A _Scott R. Shannon_, Oct 07 2024