A065355 -id:A065355 - cp's OEIS frontend

A065356 Final digits of A065355(n) (in reverse order) for sufficiently large n.

6, 8, 6, 9, 5, 0, 9, 7, 5, 9, 7, 0, 1, 7, 4, 3, 6, 6, 7, 5, 5, 3, 4, 4, 7, 4, 9, 0, 6, 9, 4, 9, 8, 6, 0, 4, 6, 7, 6, 5, 9, 1, 5, 0, 0, 2, 9, 8, 8, 7, 3, 1, 6, 2, 5, 1, 3, 1, 2, 5, 0, 2, 5, 2, 5, 7, 7, 0, 9, 9, 5, 6, 6, 9, 4, 3, 4, 1, 3, 4, 9, 9, 7, 3, 3, 4, 8, 4, 0, 2, 1, 1, 8, 3, 7, 9, 7, 1, 8, 7, 8, 6, 2, 3, 8

Offset: 0

Floor van Lamoen, Oct 31 2001

Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for sequences related to final digits of numbers

Cf. A025016, A064733, A064734.

{ for (n=0, 1000, f=1; while(f!%10^(n+1)>0, f+=1); x=sum(k=0, f, k!%10^(n+1)); a=(10*(x%10^(n+1)))\10^(n+1); if (n==0, a=3); write("b065356.txt", n, " ", 9 - a) ) } \\ Harry J. Smith, Oct 17 2009

a(n) = 9-A025016(n), n > 0. - Vladeta Jovovic, Nov 02 2001

a(60)-a(104) from Harry J. Smith, Oct 17 2009

A185009 Row sums of A051949 (differences of factorial numbers), seen as a triangle.

Original entry on oeis.org

0, 5, 45, 351, 2847, 25047, 241047, 2534247, 28984167, 358842087, 4785978087, 68453274087, 1045616538087, 16993016806887, 292825130163687, 5333909818803687, 102415654899123687, 2067588695129523687, 43785455761653171687, 970599475776544179687

Offset: 1

Olivier Gérard, Nov 02 2012

G. C. Greubel, Table of n, a(n) for n = 1..445

cf. A051949.

Other summations of differences of factorials : A206816, A206817, A065355.

Table[Plus @@ Prepend[Table[(n + 1)! - i!, {i, n, 2, -1}], (n)! - 1], {n, 0, 20}]

for(n=1,25, print1((n^2-1)*n! - sum(k=1,n-1, k!), ", ")) \\ G. C. Greubel, Jun 09 2017

a(n)= (n-1)*(n+1)*n! - sum( i!, i=1..n-1)

A343476 Numbers k whose representations in factorial base include each of the digits from 0 to d-1 exactly once, where d = A084558(k) is the number of digits of k in factorial base.

Original entry on oeis.org

0, 2, 10, 13, 14, 46, 67, 68, 77, 82, 85, 86, 238, 355, 356, 461, 466, 469, 470, 503, 526, 547, 548, 557, 562, 565, 566, 1438, 2155, 2156, 2861, 2866, 2869, 2870, 3503, 3526, 3547, 3548, 3557, 3562, 3565, 3566, 3719, 3838, 3955, 3956, 4061, 4066, 4069, 4070, 4103

Offset: 1

Amiram Eldar, Apr 16 2021

The number of terms with k > 1 digits in factorial base is 2^(k-1) - 1 = A000225(k-1).

The number of terms below k!, for k >= 1, is 2^(k-1) - (k-1) = A000325(k-1).

			2 is a term since its factorial base representation is {1, 0}.
10, 13 and 14 are terms since their factorial base representations are {1, 2, 0}, {2, 0, 1} and {2, 1, 0}, respectively.

Amiram Eldar, Table of n, a(n) for n = 1..1000
Wikipedia, Factorial number system.

A065355 is a subsequence.

Cf. A000225, A000325, A007623, A084558, A343477.

m = 7; bases = Reverse @ Range[2, m]; max = Times @@ bases; factBase[n_] := IntegerDigits[n, MixedRadix[bases]]; q[n_] := Union[(fd = factBase[n])] == Range[0, Length[fd] - 1]; Select[Range[0, max], q]

cp's OEIS Frontend

A065356 Final digits of A065355(n) (in reverse order) for sufficiently large n.

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A185009 Row sums of A051949 (differences of factorial numbers), seen as a triangle.

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A343476 Numbers k whose representations in factorial base include each of the digits from 0 to d-1 exactly once, where d = A084558(k) is the number of digits of k in factorial base.

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