A076998 -id:A076998 - cp's OEIS frontend

A076997 a(1) = 1, a(n+1) is the largest square <= n*a(n).

1, 1, 1, 1, 4, 16, 81, 529, 4225, 38025, 379456, 4173849, 50083929, 651066256, 9114902784, 136723197121, 2187571153936, 37188701848516, 669396605290000, 12718535343402256, 254370705884725824, 5341784820136403409

Offset: 1

Amarnath Murthy, Oct 26 2002

nonn

Amiram Eldar, Table of n, a(n) for n = 1..451 (terms below 10^1000)

Cf. A076998.

a[1] := 1:for i from 2 to 65 do a[i] := (floor(evalf(sqrt((i-1)*a[i-1]+1/10^120),200)))^2:od:seq(a[i],i=1..65);

a[1] = 1; a[n_] := a[n] = Floor[Sqrt[(n-1)*a[n-1]]]^2; Array[a, 22] (* Amiram Eldar, Sep 24 2023 *)
nxt[{n_,a_}]:={n+1,Floor[Sqrt[a*n]]^2}; NestList[nxt,{1,1},30][[;;,2]] (* Harvey P. Dale, Dec 02 2024 *)

Corrected and extended by Sascha Kurz, Jan 26 2003

A173956 n-th primorial modulo n.

Original entry on oeis.org

0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, 10, 0, 12, 0, 10, 0, 0, 0, 6, 20, 0, 3, 14, 0, 0, 0, 22, 0, 0, 0, 6, 0, 0, 0, 30, 0, 0, 0, 22, 30, 0, 0, 18, 21, 40, 0, 26, 0, 30, 0, 42, 0, 0, 0, 30, 0, 0, 42, 18, 0, 0, 0, 34, 0, 0, 0, 30, 0, 0, 60, 38, 0, 0, 0, 50, 12, 0, 0, 42, 0, 0, 0, 66, 0, 30, 0

Offset: 1

Carl R. White, Mar 03 2010

Very similar to A076998.

For all n, a(A013929(n)) != 0, and a(A005117(n)) = 0. - Michel Marcus, Sep 03 2013 and Antti Karttunen, Nov 20 2017

			a(9) = p(9)# mod 9 = 23# mod 9 = 2*3*5*7*11*13*17*19*23 mod 9 = 6.

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A002110, A005117 (the positions of zeros).

Differs from A076998 for the first time at n=16, where a(16) = 10, while A076998(16) = 2.

Array[Mod[Product[Prime@ i, {i, #}], #] &, 91] (* Michael De Vlieger, Nov 20 2017 *)
Module[{nn=100,prlm},prlm=FoldList[Times,Prime[Range[nn]]];Mod[ #[[1]], #[[2]]]&/@ Thread[{prlm,Range[nn]}]] (* Harvey P. Dale, May 14 2022 *)

a(n) =  prod(i=1, n, prime(i)) % n; \\ Michel Marcus, Sep 03 2013

a(n) = A002110(n) mod n. - Michel Marcus, Sep 03 2013

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A076997 a(1) = 1, a(n+1) is the largest square <= n*a(n).

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A173956 n-th primorial modulo n.

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