A083829 Palindromes k such that 3k + 1 is also a palindrome.

1, 2, 7, 77, 141, 151, 161, 242, 252, 262, 777, 7777, 14041, 14141, 14241, 15051, 15151, 15251, 16061, 16161, 16261, 24042, 24142, 24242, 25052, 25152, 25252, 26062, 26162, 26262, 77777, 777777, 1404041, 1405041, 1406041, 1414141, 1415141

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 09 2003

Keywords

• base
• nonn

Comments

From Robert Israel, Feb 23 2023: (Start)

Includes A002281. It appears that the only terms with an even number of digits are in A002281. All other terms of more than 1 digit start with 14, 15, 16, 24, 25 or 26. It also appears that no terms contain the digits 3, 8 or 9, and the only ones that contain 7 are A002281. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..6576

Crossrefs

Cf. A083830.

Programs

Maple

ispali:= proc(n) local L;
  L:= convert(n,base,10);
  L = ListTools:-Reverse(L)
end proc:
revdigs:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
palis:= proc(d) local r;
  if d::even then [seq](revdigs(r)+10^(d/2)*r,r=10^(d/2-1)..10^(d/2)-1)
  else [seq](revdigs(floor(r/10))+10^((d-1)/2)*r, r=10^((d-1)/2)..10^((d+1)/2)-1)
  fi
end proc:
[seq(op(select(t -> ispali(3*t+1), palis(d))),d=1..7)]; # Robert Israel, Feb 23 2023

Mathematica

Select[Range[15*10^5],AllTrue[{#,3#+1},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 14 2018 *)

Extensions

Corrected and extended by Ray Chandler, May 21 2003