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A259385 Palindromic numbers in bases 2 and 9 written in base 10. 16

%I

%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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Last modified July 13 07:30 EDT 2020. Contains 335676 sequences. (Running on oeis4.)