cp's OEIS Frontend

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

%I A066619 #24 Nov 08 2023 21:02:57
%S A066619 0,3,8,99,323,575,4224,5775,9999,36863,42024,999999,3055503,3640463,
%T A066619 5597955,8803088,32855823,99999999,360696063,422919224,4227990528,
%U A066619 8250997224,9999999999,30485858403,30536863503,32154945123
%N A066619 Both n and its reverse are one less than a square.
%C A066619 Numbers ending in 0 are not included except 0. - _Harry J. Smith_, Mar 13 2010
%H A066619 Harry J. Smith, <a href="/A066619/b066619.txt">Table of n, a(n) for n = 1..55</a>
%e A066619 4227990528 = 65023^2 - 1 and 8250997224 = 90835^2 - 1.
%p A066619 rev:= proc(x) local L,i;
%p A066619   L:= convert(x,base,10);
%p A066619 add(L[-i]*10^(i-1),i=1..nops(L))
%p A066619 end proc:
%p A066619 filter:= proc(x)
%p A066619   x mod 10 <> 0 and issqr(rev(x)+1)
%p A066619 end proc:
%p A066619 filter(0):= true:
%p A066619 select(filter, [seq(x^2-1,x=1..10^6)]); # _Robert Israel_, Nov 08 2023
%t A066619 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]]]
%t A066619 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 *)
%o A066619 (PARI) Rev(x)= { local(d, r=0); while (x>0, d=x%10; x\=10; r=r*10 + d); return(r) }
%o A066619 { 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
%Y A066619 Contains A028504.
%K A066619 base,nonn
%O A066619 1,2
%A A066619 _Erich Friedman_, Jan 08 2002
%E A066619 More terms from Christopher Lund (clund(AT)san.rr.com), Apr 14 2002
%E A066619 Offset changed from 0 to 1 by _Harry J. Smith_, Mar 13 2010