A262069 - OEIS

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

(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 * A370052 A082208 A201061

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