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

Author

Robert G. Wilson v, Nov 22 2014

Keywords

• nonn
• base

Links

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

Crossrefs

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

Programs

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

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 *)

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