A083831 Palindromes n such that 4n + 1 is also a palindrome.

1, 2, 8, 88, 131, 141, 232, 242, 888, 8888, 13031, 13131, 13231, 14041, 14141, 14241, 23032, 23132, 23232, 24042, 24142, 24242, 88888, 888888, 1303031, 1304031, 1313131, 1314131, 1323231, 1324231, 1403041, 1404041, 1413141, 1414141

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

Among infinite subsequences are the repdigits 8...8 = 8*(10^k-1)/9. It appears that the only terms with an even number of digits are these for even k. - Robert Israel, Apr 04 2018

Examples

			13231 and 52925 are palindromes and 4*13231+1=52925, therefore 13231 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A083829, A083830, A083832.

Programs

Maple

N:= 100: # to get the first N terms
fe:= proc(x,d) local L;
   L:= convert(x,base,10);
   add(L[j]*(10^(d-j)+10^(d+j-1)),j=1..d)
end proc:
fo:= proc(x,d) local L;
  L:= convert(x,base,10);
  add(L[j]*(10^(d-j)+10^(d+j-2)),j=2..d) + L[1]*10^(d-1);
end proc:
ispali:= proc(n) local L;
   L:= convert(n,base,10);
   L = ListTools:-Reverse(L)
end proc:
count:= 0: Res:= NULL:
for d from 1 while count < N do
  for x from 10^(d-1) to 10^d-1 while count < N do
    y:= fo(x,d);
  if ispali(4*y+1) then
     count:= count+1; Res:= Res, y;
  fi
od:
for x from 10^(d-1) to 10^d-1 while count < N do
    y:= fe(x,d);
  if ispali(4*y+1) then
     count:= count+1; Res:= Res, y;
  fi
od:
od:
Res; # Robert Israel, Apr 04 2018

Mathematica

Select[Range[15*10^5],AllTrue[{#,4#+1},PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 08 2018 *)

PARI

isok(n) = my(dn = digits(n), dm = digits(4*n+1)); (Vecrev(dn) == dn) && (Vecrev(dm) == dm); \\ Michel Marcus, Apr 04 2018

Extensions

Corrected and extended by Reinhard Zumkeller and Ray Chandler, May 18 2003