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A290024 Number of permutations in S_n that are factorials of permutations in lexicographic order. 0
1, 2, 4, 15, 72, 425, 3038 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let sigma(i), 1 <= i <= n!, be the i-th permutation in S_n in lexicographic order. a(n) = |{sigma(1)sigma(2)...sigma(i)| 1 <= i <= n!}|.

This is an S_n analog of the problem studied in the references section.

REFERENCES

B. Rokowska and A. Schinzel. Sur un problème de M. Erdős. Elem. Math., 15:84-85, 1960.

LINKS

Table of n, a(n) for n=1..7.

W. D. Banks, F. Luca, I. E. Shparlinski, H. Stichtenoth, On the Value Set of n! Modulo a Prime, Turk. J. Math., 29, (2005), 169-174.

T. Trudgian, There are no socialist primes less than 10^9, INTEGERS, 14 (2014), A63.

PROG

(PARI)

for(n=1, 7, q=vector(n!); count=0; m2=matid(n); q[1]=m2; v=vector(n); for(i=1, n, v[i]=i); v3=vector(n); for(i=1, n, v3[i]=n-i+1);

while(v3!=v, for(i=1, n-1, if(v[i]<v[i+1], a=i); for(i=a+1, n, if(v[i]> v[a], b=i))); temp=v[a]; v[a]=v[b]; v[b]=temp;

v2=vector(n-(a+1)+1); for(i=1, n-(a+1)+1, v2[i]=v[n-i+1]); for(i=a+1, n, v[i]=v2[i-a]);

m=matrix(n, n); for(i=1, n, m[v[i], i]=1); q[count+2]=m; count++);

q2=vector(n!); for(i=1, n!, m2=prod(j=1, i, q[j]); for(i=1, n!, if(q[i]==m2, a2=i)); q2[a2]++ );

a3=0; for(i=1, n!, if(q2[i]>0, a3++)); print(a3))

CROSSREFS

Sequence in context: A316661 A014517 A020110 * A292757 A182449 A140836

Adjacent sequences:  A290021 A290022 A290023 * A290025 A290026 A290027

KEYWORD

nonn,more

AUTHOR

Timothy Foo, Jul 26 2017

STATUS

approved

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Last modified May 9 22:13 EDT 2021. Contains 343746 sequences. (Running on oeis4.)