A214427 -id:A214427 - cp's OEIS frontend

A214423 Numbers n palindromic in only one base b, 2 <= b <= 10.

11, 12, 13, 14, 22, 23, 25, 29, 30, 32, 34, 35, 37, 38, 41, 42, 43, 44, 48, 49, 54, 56, 59, 60, 61, 62, 64, 66, 68, 70, 71, 72, 74, 77, 81, 83, 86, 89, 97, 101, 112, 113, 117, 118, 123, 124, 125, 126, 128, 131, 136, 138, 145, 146, 148, 153, 156, 157, 161

Offset: 1

T. D. Noe, Jul 18 2012

The base for which n is a palindrome is given in A214427.

			11 is palindromic only in base 10.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A050813, A214424, A214425, A214426 (palindromic in 0, 2-4 bases)

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

A050812(n) = 1.

A238338 Encoded bases for which A214424(n) is palindromic.

Original entry on oeis.org

13, 26, 13, 47, 28, 46, 24, 17, 25, 14, 19, 47, 17, 34, 68, 13, 24, 46, 45, 17, 46, 28, 49, 28, 56, 14, 45, 19, 45, 37, 16, 48, 59, 46, 14, 18, 15, 56, 59, 26, 36, 29, 25, 37, 69, 28, 28, 56, 47, 68, 58, 29, 35, 17, 78, 48, 49, 68, 19, 27, 79, 46, 59, 37, 28, 17

Offset: 1

T. D. Noe, Mar 07 2014

The two bases b < c are encoded as one number (b-1)*10 + (c-1). Similar to A214427 which tabulates the single base for which A214423(n) is palindromic. In the first 1000 terms, the base pairs (2,4), (2,8), (3,9), and (4,8) are most common, occurring 148, 227, 166, and 94 times, respectively. The base pair (2,3) occurs only once.

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, Mar 04 2014
Edray Herber Goins, Palindromes in different bases: a conjecture of J. Ernest Wilkins, Integers, Vol. 9 (2009), A55

Cf. A214423, A214424, A214427.

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

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

A214423 Numbers n palindromic in only one base b, 2 <= b <= 10.

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A238338 Encoded bases for which A214424(n) is palindromic.

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

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