A066619 Both n and its reverse are one less than a square.

0, 3, 8, 99, 323, 575, 4224, 5775, 9999, 36863, 42024, 999999, 3055503, 3640463, 5597955, 8803088, 32855823, 99999999, 360696063, 422919224, 4227990528, 8250997224, 9999999999, 30485858403, 30536863503, 32154945123

Offset: 1

Author

Erich Friedman, Jan 08 2002

Keywords

• base
• nonn

Comments

Numbers ending in 0 are not included except 0. - Harry J. Smith, Mar 13 2010

Examples

			4227990528 = 65023^2 - 1 and 8250997224 = 90835^2 - 1.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..55

Crossrefs

Contains A028504.

Programs

Maple

rev:= proc(x) local L,i;
  L:= convert(x,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(x)
  x mod 10 <> 0 and issqr(rev(x)+1)
end proc:
filter(0):= true:
select(filter, [seq(x^2-1,x=1..10^6)]); # Robert Israel, Nov 08 2023

Mathematica

dtn[L_] := Fold[10#1+#2&, 0, L] A={}; For[i=1, i>0, i++, t=dtn[Reverse[IntegerDigits[i^2-1]]]; If[IntegerQ[(t+1)^(1/2)]&&Mod[i^2, 10]=!=1, AppendTo[A, i^2-1]; Print[A]]]
okQ[n_]:=Module[{idn=IntegerDigits[n]},Last[idn]!=0&& IntegerQ[Sqrt[  FromDigits[ Reverse[idn]]+1]]]; Join[{0},Select[Range[180000]^2-1, okQ]]  (* Harvey P. Dale, Apr 11 2011 *)

PARI

Rev(x)= { local(d, r=0); while (x>0, d=x%10; x\=10; r=r*10 + d); return(r) }
{ n=0; for (m=0, 10^10, k=m^2 - 1; if (k%10 && issquare(Rev(k) + 1), if (m==0, k=0); write("b066619.txt", n++, " ", k); if (n==100, return)) ) } \\ Harry J. Smith, Mar 13 2010

Extensions

More terms from Christopher Lund (clund(AT)san.rr.com), Apr 14 2002

Offset changed from 0 to 1 by Harry J. Smith, Mar 13 2010