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

0, 1, 3, 5, 7, 127, 255, 273, 455, 6643, 17057, 19433, 19929, 42405, 1245161, 1405397, 1786971, 2122113, 3519339, 4210945, 67472641, 90352181, 133638015, 134978817, 271114881, 6080408749, 11022828069, 24523959661, 25636651261, 25726334461, 28829406059, 1030890430479, 1032991588623, 1085079274815, 1616662113341

Offset

1,3

Links

Giovanni Resta, Table of n, a(n) for n = 1..44

A.H.M. Smeets, Scatterplot of log_2(number is palindromic in base 2 and base b) versus b, for b in {3,5,6,7,9,10}

Index entries for sequences related to palindromes

Formula

Intersection of A006995 and A029955.

Example

273 is in the sequence because 273_10 = 333_9 = 100010001_2.

Mathematica

(* 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

Prog

(Python)
def nextpal(n, base): # m is the first palindrome successor of n in base base
    m, pl = n+1, 0
    while m > 0:
        m, pl = m//base, pl+1
    if n+1 == base**pl:
        pl = pl+1
    n = n//(base**(pl//2))+1
    m, n = n, n//(base**(pl%2))
    while n > 0:
        m, n = m*base+n%base, n//base
    return m
n, a2, a9 = 0, 0, 0
while n <= 30:
    if a2 < a9:
        a2 = nextpal(a2, 2)
    elif a9 < a2:
        a9 = nextpal(a9, 9)
    else: # a2 == a9
        print(a2, end=", ")
        a2, a9, n = nextpal(a2, 2), nextpal(a9, 9), n+1 # A.H.M. Smeets, Jun 03 2019

Crossrefs

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.

Sequence in context: A046201 A292848 A128344 * A114366 A088092 A174271

Adjacent sequences: A259382 A259383 A259384 * A259386 A259387 A259388

Keyword

nonn,base

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Status

approved