A238338 -id:A238338 - cp's OEIS frontend

A214424 Numbers that are palindromic in exactly two bases b, 2 <= b <= 10.

15, 16, 17, 18, 20, 24, 26, 27, 28, 31, 33, 36, 45, 46, 50, 51, 52, 57, 67, 73, 78, 82, 88, 91, 92, 93, 98, 99, 104, 105, 107, 109, 111, 114, 119, 127, 129, 135, 141, 142, 150, 151, 160, 170, 171, 173, 182, 185, 186, 200, 209, 212, 215, 219, 227, 246, 252

Offset: 1

T. D. Noe, Jul 18 2012

Every pair of bases occurs. The pair (2,3), for the number a(732) = 1422773, is the last to occur. Note that 1422773 = 101011011010110110101(2) = 2200021200022(3).

See A238338 for the pairs of bases. - T. D. Noe, Mar 07 2014

			15 is palindromic in bases 2 and 4: 15 = 1111_2 = 33_4.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Attila Bérczes and Volker Ziegler, On simultaneous palindromes, arXiv 1403.0787 [math.NT], 2014.
Edray Herber Goins, Palindromes in different bases: a conjecture of J. Ernest Wilkins, Integers, Vol. 9 (2009), A55.

Cf. A050813, A214423, A214425, A214426 (palindromic in 0-1 and 3-4 bases).

n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 2, AppendTo[t, n]]]; t

pal(v)=v==Vecrev(v)
is(n)=sum(b=2,10,pal(digits(n,b)))==2 \\ Charles R Greathouse IV, Mar 05 2014

A050812(a(n)) = 2.

A238893 Encoded bases for which A214425(n) is palindromic.

Original entry on oeis.org

179, 238, 135, 268, 359, 137, 137, 258, 136, 268, 237, 578, 268, 567, 589, 137, 257, 367, 269, 138, 136, 138, 489, 679, 678, 137, 268, 137, 268, 178, 179, 289, 135, 258, 147, 137, 137, 137, 128, 268, 137, 137, 268, 137, 137, 137, 137, 248, 139, 259, 137

Offset: 1

T. D. Noe, Mar 07 2014

The three bases b < c < d are encoded as one number (b-1)*100 + (c-1)*10 + (d-1). Similar to A214427 which tabulates the single base for which A214423(n) is palindromic. The vast majority of these palindromes are for the three bases (2,4,8), which encodes as 137 in this sequence.

			A214425(1) = 9. The number 9 is palindromic in 3 bases: 2, 8, and 10. Hence, a(1) = 179.

T. D. Noe, Table of n, a(n) for n = 1..1234

Cf. A214423, A214425, A214427, A238338.

n = -1; t = {}; While[Length[t] < 51, n++; If[Count[c = Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 3, d = Flatten[Position[c, True]]; AppendTo[t, 100*d[[1]] + 10*d[[2]] + d[[3]]]]]; t

cp's OEIS Frontend

A214424 Numbers that are palindromic in exactly two bases b, 2 <= b <= 10.

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