A249634 -id:A249634 - cp's OEIS frontend

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

Amiram Eldar, Aug 19 2022

			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.

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

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

Similar sequence: A249634.

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]

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

A065809 a(n) is the smallest number m > n such that m is palindromic in base n and is not palindromic in bases b with 2 <= b < n.

Original entry on oeis.org

3, 4, 25, 6, 14, 32, 54, 30, 11, 84, 39, 140, 75, 176, 102, 198, 19, 220, 147, 110, 69, 384, 175, 416, 486, 420, 58, 570, 279, 544, 429, 306, 245, 684, 296, 380, 663, 880, 615, 1134, 258, 1012, 1035, 1104, 47, 1392, 539, 1500, 1071, 1508, 53, 2106

Offset: 2

Naohiro Nomoto, Dec 06 2001

Index at which first occurrence of n occurs in A016026 when the palindrome is multidigit. Only the first two terms of A016026 are single-digit palindromes. - Robert G. Wilson v, Dec 22 2021

			From _Robert G. Wilson v_, Dec 22 2021: (Start)
a(2) = 3 since A016026(3) = 2;
a(3) = 4 since A016026(4) = 3;
a(4) = 25 since A016026(25) = 4; etc. (End)

Robert G. Wilson v, Table of n, a(n) for n = 2..10000 (first 441 terms from Robert Israel).

Cf. A016026, A065531, A249634.

N:= 100:
f:= proc(m) local k,L;
   for k from 2 to m do
     L:= convert(m,base,k);
     if L = ListTools:-Reverse(L) then return k fi
   od;
   FAIL
end proc:
V:= Array(2..N):
count:= 0:
for m from 3 while count < N-1 do
  v:= f(m);
  if v = FAIL or v > N then next fi;
  if V[v] = 0 then count:= count+1; V[v]:= m;
  fi
od:
convert(V,list); # Robert Israel, Apr 08 2019

fpb = Compile[{{n, Integer}}, Module[{b = 2, idn}, While[ Reverse[idn = IntegerDigits[n, b]] != idn, b++]; b]]; k = 3; t[] := 0; While[k < 2200, a = fpb@ k; If[ t[a] == 0, t[a] = k]; k++]; t@# & /@ Range[2, 53] (* Robert G. Wilson v, Dec 22 2021 *)

Definition edited by N. J. A. Sloane, Apr 08 2019

cp's OEIS Frontend

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.

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