A109631 -id:A109631 - cp's OEIS frontend

A109640 Indices of records in A109631.

1, 2, 5, 11, 13, 19, 23, 31, 47, 97, 101, 113, 131, 151, 181, 227, 307, 457, 907, 1009, 1129, 1289, 1511, 1801, 2251, 3001, 4507, 9001, 10007, 11251, 12889, 15013, 18013, 22501, 30011, 45007, 90001, 100003, 112501, 128591, 150001, 180001, 225023, 300007, 450001

Offset: 1

Jason Earls, Aug 04 2005

Previous name was: Values of k which are incrementally the largest values of the function: Smallest number m such that k divides (10's complement factorial of m).

Cf. A002034, A109631, A110396.

A089186 := proc(n) 10^max(1,ilog10(n)+1)-n ; end: A110396 := proc(n) mul( A089186(i),i=1..n) ; end: A109631 := proc(n) local a; for a from 1 do if A110396(a) mod n = 0 then RETURN(a) ; fi ; od: end: A109640 := proc(n) option remember ; local nprev,aprev,a ; if n = 1 then RETURN(1); else nprev := A109640(n-1) ; aprev := A109631(nprev) ; for a from nprev+1 do if A109631(a) > aprev then RETURN(a) ; fi ; od; fi ; end: for n from 1 do printf("%d, ",A109640(n)) ; od: # R. J. Mathar, Feb 12 2008

More terms from R. J. Mathar, Feb 12 2008
a(23)-a(45) from Jinyuan Wang, Aug 09 2025
New name (using comment from R. J. Mathar) from Joerg Arndt, Aug 09 2025

A109651 Numbers k such that A109631(k) + A109631(k+1) = A109631(k+2).

Original entry on oeis.org

128, 186, 954, 1462, 2106, 3535, 3679, 6439, 8176, 10032, 10284, 12632, 54008, 80600, 86994, 120006, 124352, 128554, 148863, 154260, 157624, 169799, 181830, 198789, 247080, 261199, 315560, 335825, 339890, 345676, 346112, 392886, 397734, 403040, 416890, 430492

Offset: 1

Jason Earls, Aug 05 2005

Cf. A109631, A109715.

More terms from Jinyuan Wang, Aug 09 2025

A109666 Numbers k such that A002034(k) = A109631(k).

Original entry on oeis.org

1, 2, 5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100, 120, 125, 128, 150, 175, 200, 225, 250, 256, 300, 350, 375, 384, 400, 450, 500, 512, 525, 600, 625, 640, 675, 700, 750, 768, 800, 875, 896, 900, 1000, 1024, 1050, 1125, 1152, 1200, 1250, 1280, 1350, 1375, 1400

Offset: 1

Jason Earls, Aug 06 2005

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Cf. A002034, A109631.

A109715 Numbers k such that A109631(k) - A109631(k+1) = A109631(k+2).

Original entry on oeis.org

5, 7, 71, 322, 431, 761, 1319, 1414, 2773, 3173, 8978, 10933, 11351, 14335, 15483, 21249, 26564, 27587, 41711, 46978, 48629, 49111, 50098, 67595, 68416, 74429, 80281, 82159, 86146, 88773, 99084, 110551, 116099, 127709, 138239, 150014, 170099, 172600, 172926, 199090

Offset: 1

Jason Earls, Aug 08 2005

Cf. A109631, A109651.

More terms from Jinyuan Wang, Aug 09 2025

A109650 Numbers n such that A109631(n) > n.

Original entry on oeis.org

11, 13, 19, 23, 31, 47, 97, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 181, 191, 193, 197, 199, 227, 229, 233, 239, 241, 307, 311, 313, 317, 331, 457, 461, 463, 467, 479, 487, 491, 499, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983

Offset: 1

Jason Earls, Aug 05 2005

nonn

A110396 10's complement factorial of n: a(n) = (10's complement of n)(10's complement of n-1)...(10's complement of 2)(10's complement of 1).

Original entry on oeis.org

1, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880, 32659200, 2906668800, 255786854400, 22253456332800, 1913797244620800, 162672765792768000, 13664512326592512000, 1134154523107178496000, 93000670894788636672000, 7533054342477879570432000

Offset: 0

Amarnath Murthy, Jul 29 2005

			a(3) = (10-3)*(10-2)*(10-1) = 7*8*9 = 504.

Alois P. Heinz, Table of n, a(n) for n = 0..400

Cf. A089186, A109631, A110394, A110395.

s:=proc(m) nops(convert(m,base,10)) end: for q from 1 to 120 do c[q]:=10^s(q)-q od: a:=n->product(c[i],i=1..n): seq(a(n),n=0..20); # Emeric Deutsch, Jul 31 2005
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1,
       (10^length(n)-n)*a(n-1))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 22 2015

a(n) = prod(i=1, n, 10^(1+logint(i, 10))-i); \\ Jinyuan Wang, Aug 09 2025

from functools import cache
def a(n): return 1 if n == 0 else (10**len(str(n))-n)*a(n-1)
print([a(n) for n in range(21)]) # Michael S. Branicky, Aug 13 2025

a(n) = Product_{i=1..n} c(i), where c(i) = A089186(i) is the difference between i and the next power of 10 (for example, c(13) = 100 - 13 = 87; c(100) = 1000 - 100 = 900). - Emeric Deutsch, Jul 31 2005

More terms from Emeric Deutsch, Jul 31 2005

a(0)=1 prepended by Alois P. Heinz, Aug 13 2025

cp's OEIS Frontend

A109640 Indices of records in A109631.

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A109651 Numbers k such that A109631(k) + A109631(k+1) = A109631(k+2).

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A109666 Numbers k such that A002034(k) = A109631(k).

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A109715 Numbers k such that A109631(k) - A109631(k+1) = A109631(k+2).

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A109650 Numbers n such that A109631(n) > n.

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A110396 10's complement factorial of n: a(n) = (10's complement of n)*(10's complement of n-1)*...*(10's complement of 2)*(10's complement of 1).

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A110396 10's complement factorial of n: a(n) = (10's complement of n)(10's complement of n-1)...(10's complement of 2)(10's complement of 1).