A349674 - OEIS

%I #11 Nov 24 2021 16:31:30

%S 175,1280,6,288,10,731,14,93,18,135,22,63,26,291,109,581,34,144,38,24,

%T 51,1145,46,273,50,260,335,63,58,360,62,141,110,513,224,1404,74,140,

%U 294,189,82,224,86,344,105,2410,94,417,98,176,497,56,106,76,60,189,1385,3952,100

%N a(n) is the least v-palindrome in base n.

%C A v-palindrome in base n is a number k that is not palindromic in base n, but for which A338038(k) = A338038(reverse(k) in base n).

%H Michel Marcus, <a href="/A349674/b349674.txt">Table of n, a(n) for n = 2..3000</a>

%H Daniel Tsai, <a href="https://arxiv.org/abs/2010.03151">A recurring pattern in natural numbers of a certain property</a>, arXiv:2010.03151 [math.NT], 2020.

%H Daniel Tsai, <a href="http://math.colgate.edu/~integers/v32/v32.mail.html">A recurring pattern in natural numbers of a certain property</a>, Integers (2021) Vol. 21, Article #A32.

%H Daniel Tsai, <a href="https://arxiv.org/abs/2111.10211">v-palindromes: an analogy to the palindromes</a>, arXiv:2111.10211 [math.HO], 2021. See Table 1 p. 9.

%e a(10) = A338039(1) = 18.

%t s[1] = 0; s[n_] := Plus @@ First /@ (f = FactorInteger[n]) + Plus @@ Select[Last /@ f, # > 1 &]; a[b_] := Module[{k = b+1, r}, While[!(!Divisible[k, b] && k != (r = IntegerReverse[k,b]) && s[k] == s[IntegerReverse[k, b]]), k++]; k]; Array[a, 100, 2] (* _Amiram Eldar_, Nov 24 2021 *)

%o (PARI) f(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2])); \\ A338038

%o isok(m, b) = my(r=fromdigits(Vecrev(digits(m, b)), b)); (m % b) && (m != r) && (f(r) == f(m));

%o a(n) = my(k=1); while (!isok(k, n), k++); k;

%Y Cf. A338038, A338039.

%K nonn,base

%O 2,1

%A _Michel Marcus_, Nov 24 2021