A349674 a(n) is the least v-palindrome in base n.

175, 1280, 6, 288, 10, 731, 14, 93, 18, 135, 22, 63, 26, 291, 109, 581, 34, 144, 38, 24, 51, 1145, 46, 273, 50, 260, 335, 63, 58, 360, 62, 141, 110, 513, 224, 1404, 74, 140, 294, 189, 82, 224, 86, 344, 105, 2410, 94, 417, 98, 176, 497, 56, 106, 76, 60, 189, 1385, 3952, 100

Offset: 2

Author

Michel Marcus, Nov 24 2021

Keywords

• nonn
• base

Comments

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).

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 2..3000
• Daniel Tsai, A recurring pattern in natural numbers of a certain property, arXiv:2010.03151 [math.NT], 2020.
• Daniel Tsai, A recurring pattern in natural numbers of a certain property, Integers (2021) Vol. 21, Article #A32.
• Daniel Tsai, v-palindromes: an analogy to the palindromes, arXiv:2111.10211 [math.HO], 2021. See Table 1 p. 9.

Crossrefs

Cf. A338038, A338039.

Programs

Mathematica

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 *)

PARI

f(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2])); \\ A338038
isok(m, b) = my(r=fromdigits(Vecrev(digits(m, b)), b)); (m % b) && (m != r) && (f(r) == f(m));
a(n) = my(k=1); while (!isok(k, n), k++); k;