A121347 -id:A121347 - cp's OEIS frontend

A225515 First differences of A121347.

2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2

Offset: 1

Zak Seidov, May 09 2013

nonn

Apparently a(n) = 1 or 2. From first 10000 terms, 8597 terms = 2.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A121347.

s={2}; f1=4; f2=2; k=2; Do[f1=f1*n^2; While[f2

a(n) = A121347(n+2) - A121347(n+1).

A121348 Difference between (n!)^2 and the next smaller factorial.

Original entry on oeis.org

1, 12, 456, 9360, 155520, 21772800, 1146700800, 44503603200, 11860515072000, 1237663494144000, 107797432393728000, 36342886035456000000, 6476053728774389760000, 1089563850990959984640000

Offset: 2

Hugo Pfoertner, Aug 15 2006

nonn

			a(3)=12 because the difference between (3!)^2=36 and the next smaller factorial 4!=24 is 12.

Cf. A121347 [Largest number k such that (n!)^2-k!>0].

A122221 Largest number k such that k! < (n!)^n.

Original entry on oeis.org

2, 5, 8, 13, 19, 25, 32, 41, 50, 60, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 330, 356, 383, 410, 439, 469, 499, 531, 563, 597, 631, 667, 703, 740, 779, 818, 858, 899, 942, 985, 1029, 1074, 1120, 1167, 1215, 1264, 1314, 1365, 1417

Offset: 2

Hugo Pfoertner, Sep 25 2006

			a(3)=5 because 5! = 120 is less than (3!)^3 = 216 whereas 6! = 720 > 216.

Chai Wah Wu, Table of n, a(n) for n = 2..10000

Cf. A036740, A121347, A122222, A382854.

a:=proc(n) local b: b:=proc(k) if k!<(n!)^n then k else fi end: max(seq(b(k),k=1..2200)) end: seq(a(n),n=2..67); # Emeric Deutsch, Oct 07 2006

s={};Do[k=1;Until[k!>=(n!)^n,k++]; AppendTo[s,k-1],{n,2,54}];s (* James C. McMahon, Oct 26 2024 *)

From Stirling's approximation, a(n) ~ n^2/2. A closer approximation for a(n) is n^2/2-c*n^2/log(n), where c = (1+log(0.5))/4 = A382854/2. - Johann Peters, Aug 23 2025

More terms from Emeric Deutsch, Oct 07 2006

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A225515 First differences of A121347.

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A121348 Difference between (n!)^2 and the next smaller factorial.

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A122221 Largest number k such that k! < (n!)^n.

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