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

-10, 1, 34, 89, 1516, 2425, 3536, 4849, 6364, 8081, 99100, 120121, 143144, 168169, 195196, 224225, 255256, 288289, 323324, 360361, 399400, 440441, 483484, 528529, 575576, 624625, 675676, 728729, 783784, 840841, 899900, 960961, 10231024, 10881089

Offset

0,1

Comments

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,... .

a(n+1) - a(n) = 11, 33, 55, 1427, 909, 1111, 1313, 1515, 1717, 91019, 21021, 23023, 25025, ...

= 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(n) mod 10 = periodic of period 5: repeat 1, 3, 5, 7, 9 = A141518(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

a(n) = A005563(n-1)//A000290(n) where // denotes concatenation.

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

Maple

read("transforms") :
A215268 := proc(n)
    if n = 0 then
        -10;
    else
        digcat2(n^2-1, n^2) ;
    end if;
end proc: # R. J. Mathar, Aug 07 2012
# second Maple program:
a:= n-> (s-> parse(cat(s-1, s)))(n^2):
seq(a(n), n=0..44);  # Alois P. Heinz, Jul 05 2018

Mathematica

ccd[n_]:=FromDigits[Join[IntegerDigits[n^2-1], IntegerDigits[n^2]]]; Join[{-10}, Array[ccd, 40]] (* Harvey P. Dale, Mar 02 2013 *)

Prog

(PARI) a(n) = eval(Str(n^2-1, n^2)); \\ Michel Marcus, Jul 04 2018
(Magma) [-10] cat [Seqint(Intseq(n^2) cat Intseq(n^2-1)): n in [1..50]]; // Vincenzo Librandi, Jul 04 2018

Crossrefs

Cf. A135276, A000533.

Sequence in context: A361949 A070246 A085044 * A059022 A193634 A115097

Adjacent sequences: A215265 A215266 A215267 * A215269 A215270 A215271

Keyword

sign,base,less,easy

Author

Paul Curtz, Aug 07 2012

Status

approved