A250408 Palindromic in bases 10 and 20.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 252, 6556, 6776, 7117, 10101, 12621, 20202, 22722, 30303, 1784871, 1786871, 1788871, 1913191, 1915191, 1917191, 1919191, 1444884441, 334495594433, 334843348433, 355110011553, 355746647553, 10614366341601, 14102600620141, 28095922959082, 38072044027083

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..85

Mathematica

palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; genPal[n_] := Block[{id = IntegerDigits@ n, insert = {{}, {0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}}, FromDigits@ Join[id, #, Reverse@ id] & /@ insert]; k = 1; lst = {0, 1, 2, 3,  4, 5, 6, 7, 8, 9}; While[k < 1000001, s = Select[ genPal[k], palQ[#, 20] &]; If[s != {}, AppendTo[lst, s]; Print@ s; lst = Sort@ Flatten@ lst]; k++]; lst
b1=10; b2=20; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Nov 23 2014 *)

Prog

(Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 20) eq Reverse(Intseq(n, 20))]; // Vincenzo Librandi, Nov 23 2014
(Python)
from gmpy2 import digits
def palQ(n, b): # check if n is a palindrome in base b
    s = digits(n, b)
    return s == s[::-1]
def palQgen10(l): # unordered generator of palindromes of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, 10**l):
            s = str(x)
            yield int(s+s[-2::-1])
            yield int(s+s[::-1])
A250408_list = sorted([n for n in palQgen10(6) if palQ(n, 20)])
# Chai Wah Wu, Nov 25 2014

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250409, A250410, A250411, A099165, A250412.

Sequence in context: A029967 A029968 A097855 * A029969 A029731 A248899

Adjacent sequences: A250405 A250406 A250407 * A250409 A250410 A250411

Keyword

nonn,base

Author

Robert G. Wilson v, Nov 22 2014

Status

approved