A254042 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 1's.

2, 0, 22, 47, 38, 436, 736, 2322, 3912, 47262, 123398, 263600, 679530, 725244, 8118161, 5690326

Offset: 0

Author

Martin Y. Champel, Jan 25 2015

Keywords

• nonn
• base
• more

Examples

			a(0) = 2 since 2! equals 2, which does not contain any '1'.
a(1) = 0 since 0! equals 1, which contains '1' but not '11'.
a(2) = 22 since 22! equals 1124000727777607680000, which contains '11', and 22 is the smallest integer for which this condition is met.
		

Crossrefs

Cf. A254447, A254448, A254449, A254500, A254501, A254502, A254716, A254717, A252652.

Programs

Mathematica

f[n_] := Block[{k = 0, s = ToString[(10^n - 1)/9]}, While[ Length@ StringPosition[ ToString[k!], s] != 1, j = k++]; k]; f[0] = 2; Array[f, 12, 0] (* Robert G. Wilson v, Feb 27 2015 *)

PARI

a(n)=k=0;while(k<10^4,d=digits(2*10^(#(digits(k!))+1)+10*k!);for(j=1,#d-n+1,c=0;for(i=j,j+n-1,if(d[i]==1,c++);if(d[i]!=1,c=0;break));if(c==n&&d[j+n]!=1&&d[j-1]!=1,return(k)));if(c==n,return(k));if(c!=n,k++))
for(n=1,6,print1(a(n),", ")) \\ Derek Orr, Jan 29 2015

PARI

max1s(n)=my(v=digits(n),r,t);for(i=1,#v,if(v[i]==1,t++,r=max(r,t);t=0));max(t,r)
a(n)=my(m=0); while(max1s(m!)!=n, m++); m \\ Charles R Greathouse IV, Jan 30 2015

Python

# Output doesn't include a(0).
def A254042():
    index = 1
    k = 0
    f = 1
    u = '1'
    while True:
        sf = str(f)
        if u in sf and u+'1' not in sf:
            print("A254042("+str(index)+") = " +str(k))
            index += 1
            k = 0
            f = 1
            u +='1'
        k += 1
        f *= k
    return

Extensions

a(11) from Jon E. Schoenfield, Feb 22 2015

a(12), a(13) from Jon E. Schoenfield, Mar 07 2015, Mar 08 2015

a(14)-a(15) from Bert Dobbelaere, Oct 29 2018