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A215268 Concatenation of the decimal digits of n^2-1 and n^2.

%I A215268 #35 Sep 08 2022 08:46:03
%S A215268 -10,1,34,89,1516,2425,3536,4849,6364,8081,99100,120121,143144,168169,
%T A215268 195196,224225,255256,288289,323324,360361,399400,440441,483484,
%U A215268 528529,575576,624625,675676,728729,783784,840841,899900,960961,10231024,10881089
%N A215268 Concatenation of the decimal digits of n^2-1 and n^2.
%C A215268 a(n) mod 9 has a period of length 9: repeat 8, 1, 7, 8, 4, 4, 8, 7, 1 = b(n). See A153349(n)=1,7,4,4,7,1,... .
%C A215268 a(n+1) - a(n) = 11, 33, 55, 1427, 909, 1111, 1313, 1515, 1717, 91019, 21021, 23023, 25025, ...
%C A215268       = c(n)  = 11, 3*11, 5*11, prime, 9*101, 11*101, 13*101, 15*101, 17*101, prime, 21*1001, 23*1001, ... , 61*1001, 9270063 = 3^2*11*93637, 65*10001, ... .
%C A215268 c(n) mod 10 = periodic of period 5: repeat 1, 3, 5, 7, 9 = A141518(n).
%H A215268 G. C. Greubel, <a href="/A215268/b215268.txt">Table of n, a(n) for n = 0..5000</a>
%F A215268 a(n) = A005563(n-1)//A000290(n) where // denotes concatenation.
%F A215268 a(n) = n^2+(n^2-1)*10^floor(log_10((2*n^2+1-(-1)^(2^n))/2)+1). - _Luce ETIENNE_, Sep 19 2014
%p A215268 read("transforms") :
%p A215268 A215268 := proc(n)
%p A215268     if n = 0 then
%p A215268         -10;
%p A215268     else
%p A215268         digcat2(n^2-1,n^2) ;
%p A215268     end if;
%p A215268 end proc: # _R. J. Mathar_, Aug 07 2012
%p A215268 # second Maple program:
%p A215268 a:= n-> (s-> parse(cat(s-1, s)))(n^2):
%p A215268 seq(a(n), n=0..44);  # _Alois P. Heinz_, Jul 05 2018
%t A215268 ccd[n_]:=FromDigits[Join[IntegerDigits[n^2-1],IntegerDigits[n^2]]]; Join[{-10}, Array[ccd,40]] (* _Harvey P. Dale_, Mar 02 2013 *)
%o A215268 (PARI) a(n) = eval(Str(n^2-1, n^2)); \\ _Michel Marcus_, Jul 04 2018
%o A215268 (Magma) [-10] cat [Seqint(Intseq(n^2) cat Intseq(n^2-1)): n in [1..50]]; // _Vincenzo Librandi_, Jul 04 2018
%Y A215268 Cf. A135276, A000533.
%K A215268 sign,base,less,easy
%O A215268 0,1
%A A215268 _Paul Curtz_, Aug 07 2012