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

2,1

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).

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.

Example

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

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 *)

Prog

(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;

Crossrefs

Cf. A338038, A338039.

Sequence in context: A186211 A205748 A352109 * A205470 A187420 A186212

Adjacent sequences: A349671 A349672 A349673 * A349675 A349676 A349677

Keyword

nonn,base

Author

Michel Marcus, Nov 24 2021

Status

approved