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 A349674 a(n) is the least v-palindrome in base n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 17:08 EDT 2024. Contains 375853 sequences. (Running on oeis4.)