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

1,1

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.

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

Crossrefs

Cf. A060873-A060879, A060947-A060949.

Sequence in context: A340095 A046356 A248381 * A147511 A124580 A103508

Adjacent sequences: A060871 A060872 A060873 * A060875 A060876 A060877

Keyword

nonn,base

Author

Harvey P. Dale, May 05 2001

Status

approved