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 A066619 Both n and its reverse are one less than a square. 1

%I #24 Nov 08 2023 21:02:57

%S 0,3,8,99,323,575,4224,5775,9999,36863,42024,999999,3055503,3640463,

%T 5597955,8803088,32855823,99999999,360696063,422919224,4227990528,

%U 8250997224,9999999999,30485858403,30536863503,32154945123

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

%C Numbers ending in 0 are not included except 0. - _Harry J. Smith_, Mar 13 2010

%H Harry J. Smith, <a href="/A066619/b066619.txt">Table of n, a(n) for n = 1..55</a>

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

%p rev:= proc(x) local L,i;

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

%p end proc:

%p filter:= proc(x)

%p x mod 10 <> 0 and issqr(rev(x)+1)

%p end proc:

%p filter(0):= true:

%p select(filter, [seq(x^2-1,x=1..10^6)]); # _Robert Israel_, Nov 08 2023

%t 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 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 (PARI) Rev(x)= { local(d, r=0); while (x>0, d=x%10; x\=10; r=r*10 + d); return(r) }

%o { 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 Contains A028504.

%K base,nonn

%O 1,2

%A _Erich Friedman_, Jan 08 2002

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

%E Offset changed from 0 to 1 by _Harry J. Smith_, Mar 13 2010

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Last modified December 11 09:49 EST 2023. Contains 367722 sequences. (Running on oeis4.)