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%I #25 May 01 2020 12:17:34
%S 0,1,3,5,7,127,255,273,455,6643,17057,19433,19929,42405,1245161,
%T 1405397,1786971,2122113,3519339,4210945,67472641,90352181,133638015,
%U 134978817,271114881,6080408749,11022828069,24523959661,25636651261,25726334461,28829406059,1030890430479,1032991588623,1085079274815,1616662113341
%N Palindromic numbers in bases 2 and 9 written in base 10.
%H Giovanni Resta, <a href="/A259385/b259385.txt">Table of n, a(n) for n = 1..44</a>
%H A.H.M. Smeets, <a href="/A259385/a259385.gif">Scatterplot of log_2(number is palindromic in base 2 and base b) versus b, for b in {3,5,6,7,9,10}</a>
%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%F Intersection of A006995 and A029955.
%e 273 is in the sequence because 273_10 = 333_9 = 100010001_2.
%t (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 9]; If[palQ[pp, 2], AppendTo[lst, pp]; Print[pp]]; k++]; lst
%o (Python)
%o def nextpal(n, base): # m is the first palindrome successor of n in base base
%o m, pl = n+1, 0
%o while m > 0:
%o m, pl = m//base, pl+1
%o if n+1 == base**pl:
%o pl = pl+1
%o n = n//(base**(pl//2))+1
%o m, n = n, n//(base**(pl%2))
%o while n > 0:
%o m, n = m*base+n%base, n//base
%o return m
%o n, a2, a9 = 0, 0, 0
%o while n <= 30:
%o if a2 < a9:
%o a2 = nextpal(a2,2)
%o elif a9 < a2:
%o a9 = nextpal(a9, 9)
%o else: # a2 == a9
%o print(a2, end=",")
%o a2, a9, n = nextpal(a2,2), nextpal(a9,9), n+1 # _A.H.M. Smeets_, Jun 03 2019
%Y Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.
%K nonn,base
%O 1,3
%A Eric A. Schmidt and _Robert G. Wilson v_, Jul 16 2015
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