A250410 Numbers palindromic in bases 10 and 25.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 494, 626, 676, 1001, 6886, 7887, 8338, 9339, 622226, 626626, 2828282, 2859582, 3304033, 3309033, 3330333, 3335333, 3361633, 3366633, 3392933, 3397933, 6603066, 6608066, 6634366, 6639366, 8986898, 9400049, 9405049, 9431349, 9436349, 9462649, 9467649, 9493949, 9498949

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..94 (first 82 terms from Chai Wah Wu)

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250411, A099165, A250412.

Programs

Magma

[n: n in [0..10000000] | Intseq(n) eq Reverse(Intseq(n))and Intseq(n, 25) eq Reverse(Intseq(n, 25))]; // 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[#, 25] &]; If[s != {}, AppendTo[lst, s]; Print@ s; lst = Sort@ Flatten@ lst]; k++]; lst

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])
A250410_list = sorted([n for n in palQgen10(6) if palQ(n,25)])
# Chai Wah Wu, Nov 25 2014