%I #21 Apr 04 2018 10:06:34

%S 1,2,8,88,131,141,232,242,888,8888,13031,13131,13231,14041,14141,

%T 14241,23032,23132,23232,24042,24142,24242,88888,888888,1303031,

%U 1304031,1313131,1314131,1323231,1324231,1403041,1404041,1413141,1414141

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

%C 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

%H Robert Israel, <a href="/A083831/b083831.txt">Table of n, a(n) for n = 1..1000</a>

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

%p N:= 100: # to get the first N terms

%p fe:= proc(x,d) local L;

%p L:= convert(x,base,10);

%p add(L[j]*(10^(d-j)+10^(d+j-1)),j=1..d)

%p end proc:

%p fo:= proc(x,d) local L;

%p L:= convert(x,base,10);

%p add(L[j]*(10^(d-j)+10^(d+j-2)),j=2..d) + L[1]*10^(d-1);

%p end proc:

%p ispali:= proc(n) local L;

%p L:= convert(n,base,10);

%p L = ListTools:-Reverse(L)

%p end proc:

%p count:= 0: Res:= NULL:

%p for d from 1 while count < N do

%p for x from 10^(d-1) to 10^d-1 while count < N do

%p y:= fo(x,d);

%p if ispali(4*y+1) then

%p count:= count+1; Res:= Res, y;

%p fi

%p od:

%p for x from 10^(d-1) to 10^d-1 while count < N do

%p y:= fe(x,d);

%p if ispali(4*y+1) then

%p count:= count+1; Res:= Res, y;

%p fi

%p od:

%p od:

%p Res; # _Robert Israel_, Apr 04 2018

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

%o (PARI) isok(n) = my(dn = digits(n), dm = digits(4*n+1)); (Vecrev(dn) == dn) && (Vecrev(dm) == dm); \\ _Michel Marcus_, Apr 04 2018

%Y Cf. A083829, A083830, A083832.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 09 2003

%E Corrected and extended by _Reinhard Zumkeller_ and _Ray Chandler_, May 18 2003