A249157 -id:A249157 - cp's OEIS frontend

A249156 Palindromic in bases 5 and 7.

0, 1, 2, 3, 4, 6, 24, 57, 78, 114, 342, 624, 856, 1432, 10308, 12654, 27616, 100056, 537856, 593836, 769621, 1434168, 1473368, 1636104, 1823544, 1862744, 17968646, 18108296, 22412057, 34713713, 34853363, 39280254, 159690408, 663706192

Offset: 1

Ray Chandler, Oct 27 2014

Intersection of A029952 and A029954.

			114 is a term since 114 = 424 base 5 and 114 = 222 base 7.

G. Resta, Table of n, a(n) for n = 1..72 (first 60 terms from Ray Chandler)
Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Cf. A007632, A060792, A249155, A249157, A249158.

palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,5]&&palQ[#,7]&]

isok(n) = my(df = digits(n, 5), ds = digits(n, 7)); (Vecrev(df)==df) && (Vecrev(ds)==ds); \\ Michel Marcus, Oct 31 2017

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 palQgen(l,b): # unordered generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1,b**l):
            s = digits(x,b)
            yield int(s+s[-2::-1],b)
            yield int(s+s[::-1],b)
A249156_list = sorted([n for n in palQgen(8,5) if palQ(n,7)]) # Chai Wah Wu, Nov 25 2014

A249155 Palindromic in bases 6 and 15.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 14, 80, 160, 301, 602, 693, 994, 1295, 1627, 1777, 2365, 2666, 5296, 5776, 6256, 17360, 34720, 51301, 52201, 105092, 155493, 209284, 587846, 735644, 7904800, 11495701, 80005507, 80469907, 83165017, 89731777, 90196177

Offset: 1

Ray Chandler, Oct 27 2014

Intersection of A029953 and A029960.

			301 is a term since 301 = 1221 base 6 and 301 = 151 base 15.

Ray Chandler and Chai Wah Wu, Table of n, a(n) for n = 1..71 (terms < 6^28). First 65 terms from Ray Chandler.
Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Cf. A007632, A060792, A249156, A249157, A249158.

palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[10^6] - 1, palQ[#, 6] && palQ[#, 15] &]

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 palQgen(l, b): # generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, l+1):
            for y in range(b**(x-1), b**x):
                s = digits(y, b)
                yield int(s+s[-2::-1], b)
            for y in range(b**(x-1), b**x):
                s = digits(y, b)
                yield int(s+s[::-1], b)
A249155_list = [n for n in palQgen(8, 6) if palQ(n, 15)] # Chai Wah Wu, Nov 29 2014

A249158 Palindromic in bases 7 and 29.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 16, 24, 150, 300, 5952, 7752, 7955, 9755, 9958, 11904, 13704, 13907, 14110, 15707, 15910, 392850, 751043, 4585544, 12737804, 12828748, 16380296, 19289406, 19380350, 20228253, 33115710, 395849700, 1339182534

Offset: 1

Ray Chandler, Oct 27 2014

			150 is a term since 150 = 303 base 7 and 150 = 55 base 27.

Ray Chandler, Table of n, a(n) for n = 1..80 (terms < 10^18)
Attila Bérczes and Volker Ziegler, On Simultaneous Palindromes, arXiv:1403.0787 [math.NT], 2014.

Cf. A007632, A060792, A249155, A249156, A249157.

palQ[n_Integer,base_Integer]:=Block[{idn=IntegerDigits[n,base]},idn==Reverse[idn]];Select[Range[10^6]-1,palQ[#,7]&&palQ[#,29]&]

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 palQgen(l, b): # unordered generator of palindromes in base b of length <= 2*l
    if l > 0:
        yield 0
        for x in range(1, b**l):
            s = digits(x, b)
            yield int(s+s[-2::-1], b)
            yield int(s+s[::-1], b)
A249158_list = sorted([n for n in palQgen(8,7) if palQ(n,29)])
# Chai Wah Wu, Nov 25 2014

cp's OEIS Frontend

A249156 Palindromic in bases 5 and 7.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A249155 Palindromic in bases 6 and 15.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

A249158 Palindromic in bases 7 and 29.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Python