A060112 -id:A060112 - cp's OEIS frontend

A265334 Numbers that are >= k! but < 2*k! for some k; numbers whose factorial base representation (A007623) begins with digit "1".

1, 2, 3, 6, 7, 8, 9, 10, 11, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150

Offset: 1

Antti Karttunen, Dec 25 2015

nonn

Numbers k for which A099563(k) = 1.

Numbers k for which A265333(k) = 1.

			1 is present as 1 >= 1! but < 2*1!
2 is present as 2 >= 2! but < 2*2!
3 is present as 3 >= 2! but < 2*2!
4 is not present as 4 >= 2! but not < 2*2! (and not >= 3!).

Antti Karttunen, Table of n, a(n) for n = 1..5915
Index entries for sequences related to factorial base representation

Cf. A007623, A099563, A265333 (characteristic function).
Cf. A059590, A060112 (subsequences).
Cf. also A265897, A265898.

A014489 Positions of involutions (permutations whose square is the identity) in reverse colexicographic order (A055089/A195663).

Original entry on oeis.org

0, 1, 2, 5, 6, 7, 14, 16, 21, 23, 24, 25, 26, 29, 54, 55, 60, 67, 80, 82, 86, 94, 105, 107, 111, 119, 120, 121, 122, 125, 126, 127, 134, 136, 141, 143, 264, 265, 266, 269, 288, 289, 314, 316, 339, 341, 390, 391, 396, 403, 414, 415, 444, 450, 469

Offset: 0

Wouter Meeussen

nonn

Robert Israel, Table of n, a(n) for n = 0..3996

Positions of zeros in A261099.
From a(1)=1 onward also positions of 2's in A055092.
Subsequences: A060112, A064640.
Cf. A055089, A195663.
Cf. also A261220.

N:= 100: # to get a(0) to a(N)
M:= 0: A[0]:= 0: count:= 0:
for m from 2 while count < N do
  P:= remove(t -> t[1]=1, combinat:-permute(m));
  P:= map(t -> ListTools:-Reverse(subs([seq(i=m+1-i,i=1..m)],t)),P);
  R:= select(t -> max(map(nops,convert(P[t],disjcyc))) = 2, [$1..nops(P)]);
  for r in R do
     count:= count+1;
     A[count]:= r+M;
     if count = N then break fi;
  od:
  M:= M + nops(P);
od:
seq(A[i],i=0..count); # Robert Israel, Oct 28 2015

Name changed by Antti Karttunen, Aug 30 2015

cp's OEIS Frontend

A265334 Numbers that are >= k! but < 2*k! for some k; numbers whose factorial base representation (A007623) begins with digit "1".

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A014489 Positions of involutions (permutations whose square is the identity) in reverse colexicographic order (A055089/A195663).

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