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A262069 Palindromes in base 10 that are also palindromes in base 60. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

EXAMPLE

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).

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 *)

PROG

(Haskell)

-- import Data.List.Ordered (isect)

a262069 n = a262069_list !! (n-1)

a262069_list = isect a002113_list a262065_list

(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

(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

(PARI) ispal(v) = v == Vecrev(v);

isok(n) = ispal(digits(n)) && ispal(digits(n, 60)); \\ Michel Marcus, Sep 11 2015

CROSSREFS

Intersection of A002113 and A262065.

Sequence in context: A032573 A190217 A222620 * A082208 A201061 A099165

Adjacent sequences:  A262066 A262067 A262068 * A262070 A262071 A262072

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Sep 10 2015

EXTENSIONS

More terms from Chai Wah Wu, Sep 10 2015

STATUS

approved

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Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)