OFFSET
1,2
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
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
EXAMPLE
13231 and 52925 are palindromes and 4*13231+1=52925, therefore 13231 is a term.
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 *)
PROG
(PARI) isok(n) = my(dn = digits(n), dm = digits(4*n+1)); (Vecrev(dn) == dn) && (Vecrev(dm) == dm); \\ Michel Marcus, Apr 04 2018
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 09 2003
EXTENSIONS
Corrected and extended by Reinhard Zumkeller and Ray Chandler, May 18 2003
STATUS
approved