A356640 a(n) is the least number k such that the least base in which k is a Niven number is n, i.e., A356552(k) = n, or -1 if no such k exists.

1, 3, 50, 5, 44, 7, 161, 119, 201, 11, 253, 13, 494, 226, 1444, 17, 799, 19, 437, 1189, 957, 23, 1081, 2263, 755, 767, 927, 29, 932, 31, 1147, 5141, 1191, 1226, 2009, 37, 1517, 1522, 1641, 41, 1927, 43, 2021, 2026, 2164, 47, 2491, 4559, 5001, 2602, 2757, 53, 2972

Offset: 2

Author

Amiram Eldar, Aug 19 2022

Keywords

• nonn
• base

Examples

			a(3) = 3 since 3 is a Niven number in base 3 and in no other base smaller than 3. 1 and 2 are also Niven numbers in base 3, but they are also Niven numbers in base 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..1368

Crossrefs

Cf. A005349, A049445, A064150, A064438, A064481, A356552.

Similar sequence: A249634.

Programs

Mathematica

f[n_] := Module[{b = 2}, While[! Divisible[n, Plus @@ IntegerDigits[n, b]], b++]; b]; A356640[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] - 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; A356640[50, 10^4]

Formula

a(p) = p for an odd prime p.