A262069 Palindromes in base 10 that are also palindromes in base 60.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 55155, 55455, 55755, 57075, 57375, 113311, 148841, 2796972, 8372738, 11166111, 14033041, 26233262, 28933982, 150050051, 151141151, 152070251, 152232251, 153161351, 153323351, 154252451, 154414451, 155343551, 155505551
Offset: 1
Examples
n = 22: 41*60^2 + 20*60^1 + 41*60^0 = A262065(2541) = A002113(1148) = 148841 = a(22); n = 27: 2*60^4 + 1*60^3 + 27*60^2 + 1*60^1 + 2*60^0 = A262065(7348) = A002113(12623) = 26233262 = a(27).
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..82
- Eric Weisstein's World of Mathematics, Palindromic Number
- Eric Weisstein's World of Mathematics, Sexagesimal
- Wikipedia, Palindromic number
- Wikipedia, Sexagesimal
- Index entries for sequences related to palindromes
Programs
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Haskell
-- import Data.List.Ordered (isect) a262069 n = a262069_list !! (n-1) a262069_list = isect a002113_list a262065_list
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Magma
[n: n in [0..2*10^7] | Intseq(n, 60) eq Reverse(Intseq(n, 60)) and Intseq(n, 10) eq Reverse(Intseq(n, 10))]; // Vincenzo Librandi, Sep 11 2015
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Mathematica
palQ[n_Integer, base_Integer]:=Module[{idn=IntegerDigits[n, base]}, idn==Reverse[idn]]; Select[Range[10^6], palQ[#, 10]&& palQ[#, 60] &] (* Vincenzo Librandi, Sep 11 2015 *) -
PARI
ispal(v) = v == Vecrev(v); isok(n) = ispal(digits(n)) && ispal(digits(n,60)); \\ Michel Marcus, Sep 11 2015
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Python
def palgen(l,b=10): # generator of palindromes in base b of length <= 2*l if l > 0: yield 0 for x in range(1,l+1): n = b**(x-1) n2 = n*b for y in range(n,n2): k, m = y//b, 0 while k >= b: k, r = divmod(k,b) m = b*m + r yield y*n + b*m + k for y in range(n,n2): k, m = y, 0 while k >= b: k, r = divmod(k,b) m = b*m + r yield y*n2 + b*m + k A262069_list = [n for n in palgen(5,60) if str(n) == str(n)[::-1]] # Chai Wah Wu, Sep 10 2015
Extensions
More terms from Chai Wah Wu, Sep 10 2015