A116670 -id:A116670 - cp's OEIS frontend

A116695 Digit not appearing in A116670(n).

9, 8, 9, 7, 8, 7, 9, 8, 9, 6, 8, 6, 9, 7, 9, 6, 7, 6, 8, 7, 8, 6, 7, 6, 9, 8, 9, 7, 8, 7, 9, 8, 9, 5, 8, 5, 9, 7, 9, 5, 7, 5, 8, 7, 8, 5, 7, 5, 9, 8, 9, 6, 8, 6, 9, 8, 9, 5, 8, 5, 9, 6, 9, 5, 6, 5, 8, 6, 8, 5, 6, 5, 9, 7, 9, 6, 7, 6, 9, 7, 9, 5, 7, 5, 9, 6, 9, 5, 6, 5, 7, 6, 7, 5, 6, 5, 8, 7, 8, 6, 7, 6, 8, 7, 8

Offset: 1

Rick L. Shepherd, Feb 23 2006

			a(1) = 9 as all decimal digits but 9 appear in A116670(1) = 102345678.

Cf. A116670 (Numbers with all but one decimal digit).

Offset adapted to the offset of A116670 by Alois P. Heinz, Apr 08 2022

A219743 Number for which the number of distinct base 10 digits is 8.

Original entry on oeis.org

10234567, 10234568, 10234569, 10234576, 10234578, 10234579, 10234586, 10234587, 10234589, 10234596, 10234597, 10234598, 10234657, 10234658, 10234659, 10234675, 10234678, 10234679, 10234685, 10234687, 10234689, 10234695, 10234697, 10234698

Offset: 1

Jonathan Vos Post, Dec 05 2012

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A010785 (1 digits), A031955 (2 digits), A031962 (3 digits), A031969 (4 digits), A031987 (5 digits), A220076 (6 digits), A218019 (7 digits), A116670 (9 digits), A171102 (10 digits).

Select[Range[10^7, 10^7 + 1000000], Length[Union[IntegerDigits[#]]] == 8 &] (* T. D. Noe, Dec 05 2012 *)

Corrected and extended by T. D. Noe, Dec 05 2012

A337127 Table with 10 columns read by rows: T(n, k) is the number of n-digit positive integers with exactly k distinct base 10 digits (0 < k <= 10).

Original entry on oeis.org

9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 81, 0, 0, 0, 0, 0, 0, 0, 0, 9, 243, 648, 0, 0, 0, 0, 0, 0, 0, 9, 567, 3888, 4536, 0, 0, 0, 0, 0, 0, 9, 1215, 16200, 45360, 27216, 0, 0, 0, 0, 0, 9, 2511, 58320, 294840, 408240, 136080, 0, 0, 0, 0, 9, 5103, 195048, 1587600, 3810240, 2857680, 544320, 0, 0, 0

Offset: 1

Stefano Spezia, Aug 17 2020

			The table T(n, k) begins:
9     0      0       0       0       0  0  0  0  0
9    81      0       0       0       0  0  0  0  0
9   243    648       0       0       0  0  0  0  0
9   567   3888    4536       0       0  0  0  0  0
9  1215  16200   45360   27216       0  0  0  0  0
9  2511  58320  294840  408240  136080  0  0  0  0
...

Index entries for sequences related to digits.

Cf. A010785, A031955, A031962, A031969, A031987, A116670, A171102, A218019, A219743, A220076.

Cf. A010734, A048993, A052268 (row sums), A073531 (diagonal), A180599 (k = 1), A335843 (k = 2), A337313 (k = 3).

T[n_,k_]:=9Pochhammer[11-k,k-1]/k!*n!*Coefficient[Series[(Exp[x]-1)^k,{x,0,n}],x,n]; Table[T[n,k],{n,7},{k,10}]//Flatten

T(n, k) = 9*Pochhammer(11-k, k-1)*n! * [x^n] (exp(x) - 1)^k/k!.
T(n, k) = 9*Pochhammer(11-k, k-1) * [x^n] x^k/Product_{j=1..k} (1-j*x).
T(n, k) = 9*Pochhammer(11-k, k-1)*S2(n, k) where S2(n, k) = A048993(n, k) are the Stirling numbers of the 2nd kind.

A227795 For each base, b, beginning with binary, the number of (b-1)-digit primes with one copy of each digit save one.

Original entry on oeis.org

0, 3, 1, 9, 52, 283, 2113, 16142, 145227, 1359133, 15000161, 172888810, 2217146126

Offset: 2

James G. Merickel, Sep 23 2013

Note that only decimal 2, 11 and 19 are representable in some base using a copy of each digit in that base (base 2 for the first and base 3 for the others), as a number written in base b with a single copy of each digit is congruent to either 0 or (b-1)/2 modulo b-1.

			In base 3, 10, 12 and 21 are primes: Decimal 3, 5 and 7.  In base 4, of the possibilities only 103 is prime: Decimal 19.

Cf. A073643, A116670.

\\ Starts at base 4 and prints in form 'base:count', bases 2 and 3 done by hand.
{
b=4;while(1,
c=0;for(i=1,b!,perm=numtoperm(b,i);
if(perm[b-1]!=1,
if(gcd(b,perm[1]-1)==1,
if(gcd(b-1,perm[b]-1)==1,
n=sum(j=1,b-1,(perm[j]-1)*b^(j-1));
if(ispseudoprime(n),c++)))));
print1(b":"c"\n");b++)
}

a(14) added by James G. Merickel, Oct 14 2013

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A116695 Digit not appearing in A116670(n).

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A219743 Number for which the number of distinct base 10 digits is 8.

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A337127 Table with 10 columns read by rows: T(n, k) is the number of n-digit positive integers with exactly k distinct base 10 digits (0 < k <= 10).

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A227795 For each base, b, beginning with binary, the number of (b-1)-digit primes with one copy of each digit save one.

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