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A249156 Palindromic in bases 5 and 7. 20
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Intersection of A029952 and A029954.
LINKS
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.
EXAMPLE
114 is a term since 114 = 424 base 5 and 114 = 222 base 7.
MATHEMATICA
palQ[n_Integer, base_Integer]:=Block[{idn=IntegerDigits[n, base]}, idn==Reverse[idn]]; Select[Range[10^6]-1, palQ[#, 5]&&palQ[#, 7]&]
PROG
(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 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
(PARI) isok(n) = my(df = digits(n, 5), ds = digits(n, 7)); (Vecrev(df)==df) && (Vecrev(ds)==ds); \\ Michel Marcus, Oct 31 2017
CROSSREFS
Sequence in context: A329577 A217442 A065199 * A033179 A067244 A084811
KEYWORD
nonn,base
AUTHOR
Ray Chandler, Oct 27 2014
STATUS
approved

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Last modified May 21 00:58 EDT 2024. Contains 372720 sequences. (Running on oeis4.)