A043041 Base-10 palindromes that start with 6.

6, 66, 606, 616, 626, 636, 646, 656, 666, 676, 686, 696, 6006, 6116, 6226, 6336, 6446, 6556, 6666, 6776, 6886, 6996, 60006, 60106, 60206, 60306, 60406, 60506, 60606, 60706, 60806, 60906, 61016, 61116, 61216, 61316, 61416, 61516, 61616, 61716, 61816, 61916, 62026

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Jaroslav Krizek and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2222 terms from Jaroslav Krizek)

Crossrefs

Intersection of A002113 and A217399.

Programs

Mathematica

palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; Select[Range[0, 100000], IntegerDigits[#][[1]] == 6 && palQ[#, 10] &] (* T. D. Noe, Mar 12 2013 *)
Select[Flatten[Table[Range[6*10^n,7*10^n-1],{n,0,4}]],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 25 2017 *)

PARI

nxt2113(n)={my(d=digits(n)); i=(#d+1)\2; while(i&&d[i]==9, d[i]=0; d[#d+1-i]=0; i--); if(i, d[i]++; d[#d+1-i]=d[i], d=vector(#d+1); d[1]=d[#d]=1); d}
nxt(n) = my(d = nxt2113(n)); if(d[1]==6, fromdigits(d), 6*(10^#d+1))
print1(a = 6, ", "); for (n=1, 30, print1(a = nxt(a), ", ")) \\ David A. Corneth, Jun 25 2017

Formula

a(n) = A002113(k) iff k starts with 7 or 16. - David A. Corneth, Jun 25 2017