A060874 Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.

9, 15, 28, 40, 52, 56, 65, 68, 80, 85, 105, 125, 126, 130, 150, 156, 170, 186, 190, 195, 215, 216, 217, 235, 246, 252, 255, 259, 282, 301, 312, 342, 343, 344, 372, 378, 385, 400, 408, 427, 434, 438, 456, 468, 476, 498, 504, 512, 513, 518, 534

Offset: 1

Author

Harvey P. Dale, May 05 2001

Keywords

• nonn
• base

Comments

All numbers are intrinsic 1- and 2-palindromes, almost all numbers are intrinsic 3-palindromes and very few numbers are intrinsic k-palindromes for k >= 4.

Links

• Robert Israel and Peter Kagey, Table of n, a(n) for n = 1..10000 (1..1000 from Peter Kagey)
• A. J. Di Scala and M. Sombra, Intrinsic Palindromic Numbers, arXiv:math/0105022 [math.GM], 2001.
• A. J. Di Scala and M. Sombra, Intrinsic Palindromes, Fib. Quart. 42, no. 1, Feb. 2004, pp. 76-81.

Crossrefs

Cf. A060873-A060879, A060947-A060949.

Programs

Maple

N:= 10^4: # to get all terms <= N
S:= {}:
for b from 2 to floor(N^(1/3)) do
  S:= S union {seq(seq((b^3+1)*i+(b^2+b)*j,j=0..b-1),i=1..b-1)}
od:
sort(convert(select(`<=`,S,N),list)); # Robert Israel, May 23 2016