A018799 -id:A018799 - cp's OEIS frontend

A279089 Record values of A018799 (Smallest nonnegative integer m such that m! begins with n in base 10).

0, 2, 9, 14, 96, 113, 205, 245, 351, 369, 597, 629, 716, 1461, 1645, 1677, 1695, 3258, 3830, 4055, 5153, 7261, 8769, 11376, 12745, 18035, 19336, 20165, 21384, 27152, 34911, 39414, 44141, 46666, 48358, 54689, 57751, 60215, 63080, 71922, 83906, 87535, 102757

Offset: 1

Jon E. Schoenfield, Jan 30 2017

For the indices at which these values occur in A018799, see A279090.

Cf. A018799, A279090.

A279090 Indices at which record values occur in A018799 (Smallest nonnegative integer m such that m! begins with n in base 10).

Original entry on oeis.org

1, 2, 3, 8, 9, 22, 27, 34, 43, 45, 58, 95, 97, 107, 153, 174, 212, 262, 311, 348, 381, 409, 590, 676, 841, 1204, 1619, 1684, 1709, 1735, 2357, 2418, 3213, 3374, 4449, 4459, 4596, 4620, 4683, 5140, 5310, 6039, 6495

Offset: 1

Jon E. Schoenfield, Jan 30 2017

For the record values that occur in A018799 at these indices, see A279089.

Cf. A018799, A279089.

A008905 Leading digit of n!.

Original entry on oeis.org

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

Offset: 0

Russ Cox

Kunoff proved that the distribution of terms of this sequence follows Benford's law, i.e., the asymptotic density of terms with value d (between 1 and 9) is log_10(1+1/d). - Amiram Eldar, Sep 23 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.
Index entries for sequences related to factorial numbers

Cf. A000966, A000142, A018799, A202021 (leading digit of (10^n)!), A213201.

a008905 = a000030 . a000142  -- Reinhard Zumkeller, Apr 08 2012

f[n_] := Quotient[n!, 10^Floor@ Log[10, n!]]; Array[f, 105, 0]

a(n) = A000030(A000142(n)). - Reinhard Zumkeller, Apr 08 2012

Two less-efficient Mathematica codings removed by Robert G. Wilson v, Nov 05 2010

A076219 Smallest positive integer m such that m! begins with n in base 10.

Original entry on oeis.org

1, 2, 9, 8, 7, 3, 6, 14, 96, 27, 22, 5, 15, 42, 25, 89, 69, 76, 63, 16, 87, 113, 54, 4, 23, 30, 205, 85, 34, 28, 62, 164, 41, 245, 17, 9, 36, 128, 11, 8, 185, 53, 351, 73, 369, 118, 12, 265, 129, 7, 21, 38, 235, 66, 46, 258, 81, 597, 279, 43, 72, 13, 559, 18, 203, 120, 311

Offset: 1

Lekraj Beedassy, Nov 04 2002

			We have a(5) = 7 since 7! = 5040 and no smaller factorial number begins with 5 in base 10.

Apart from leading term, identical to A018799.

More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Jan 13 2005

A155891 Least positive integer such that a(n)! starts with n, both written in binary.

Original entry on oeis.org

1, 2, 3, 7, 6, 3, 5, 20, 7, 14, 6, 4, 10, 12, 5, 20, 27, 50, 7, 14, 23, 6, 13, 4, 25, 30, 10, 12, 51, 5, 63, 24, 20, 36, 27, 50, 59, 11, 7, 14, 26, 75, 23, 9, 6, 13, 49, 71, 144, 31, 25, 30, 199, 19, 10, 46, 12, 51, 83, 5, 28, 73, 63, 62, 24, 54, 20, 36, 67, 27, 40, 74, 50, 59, 124

Offset: 1

M. F. Hasler, Feb 01 2009

			a(7) = 5 since 7 = 111_2 (i.e., written in base 2) and 5! = 1111000_2 is the least factorial to have 111 as its most significant binary digits.

Nick Hobson, Table of n, a(n) for n = 1..16383
Nick Hobson, C program.

Cf. A018799, A076219.

C
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See Links section.
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A155891(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=2 )); k}

A155892 Least positive integer such that a(n)! starts with n, both written in base 3.

Original entry on oeis.org

1, 2, 12, 5, 13, 3, 19, 4, 31, 18, 12, 21, 5, 33, 17, 13, 34, 8, 38, 7, 19, 92, 24, 4, 11, 6, 46, 39, 31, 22, 18, 77, 12, 55, 32, 75, 21, 52, 74, 5, 15, 33, 61, 122, 166, 17, 47, 13, 65, 54, 49, 148, 34, 71, 8, 117, 107, 60, 38, 51, 10, 7, 111, 25, 19, 92, 123, 128, 29, 24, 56, 99

Offset: 1

M. F. Hasler, Feb 01 2009

			a(4) = 5 since 4 = 11[3] (i.e. written in base 2) and 5! = 11110[3] is the least factorial to have 11 as most significant digits in base 3.

Cf. A155891, A018799, A076219.

A155892(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=3 )); k}

A155894 Least positive integer such that a(n)! starts with n, both written in base 16.

Original entry on oeis.org

1, 2, 10, 36, 9, 3, 5, 24, 8, 43, 82, 25, 30, 46, 64, 62, 60, 68, 7, 14, 70, 18, 13, 4, 31, 272, 19, 12, 97, 35, 161, 140, 20, 86, 27, 74, 131, 11, 502, 234, 47, 181, 386, 21, 6, 996, 52, 232, 144, 32, 393, 189, 199, 281, 10, 490, 39, 154, 83, 22, 28, 577, 63, 65, 88, 61, 115

Offset: 1

M. F. Hasler, Feb 01 2009

Nick Hobson, Table of n, a(n) for n = 1..4095
Nick Hobson, C program.

Cf. A155891, A155892, A155893, A018799, A076219.

C
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See Links section.
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A155894(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=16 )); k}

A018854 Smallest factorial that begins with n.

Original entry on oeis.org

1, 2, 362880, 40320, 5040, 6, 720, 87178291200

Offset: 1

David W. Wilson

a(9) = 96! is too large to include, see b-file.

Seiichi Manyama, Table of n, a(n) for n = 1..57

Cf. A018799.

a(n) = A018799(n)!. - Seiichi Manyama, Jan 29 2017

A155893 Least positive integer such that a(n)! starts with n, both written in base 8.

Original entry on oeis.org

1, 2, 4, 16, 13, 3, 46, 27, 7, 14, 6, 32, 10, 39, 5, 20, 86, 50, 11, 26, 121, 18, 38, 4, 31, 199, 34, 12, 139, 28, 63, 62, 61, 67, 60, 125, 59, 16, 37, 58, 47, 108, 23, 21, 41, 13, 112, 71, 194, 56, 25, 30, 302, 19, 166, 46, 55, 150, 83, 116, 219, 73, 90, 140, 164, 54, 207

Offset: 1

M. F. Hasler, Feb 01 2009

Cf. A155891, A155892, A018799, A076219.

A155893(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=8 )); k}

A155895 Least positive integer such that a(n)! starts with n, both written in base 5.

Original entry on oeis.org

1, 2, 17, 4, 6, 3, 29, 7, 10, 19, 31, 8, 18, 14, 37, 61, 81, 17, 33, 11, 63, 94, 9, 4, 13, 24, 16, 6, 27, 22, 52, 152, 28, 21, 143, 45, 35, 29, 67, 7, 62, 15, 247, 181, 193, 10, 105, 48, 12, 97, 19, 167, 36, 72, 146, 75, 31, 391, 69, 40, 186, 486, 133, 8, 57, 46, 18, 103, 115

Offset: 1

M. F. Hasler, Feb 01 2009

			a(3) = 17 since 17! is the least factorial to start with digit "3" when written in base 5. a(5) = 6 since 5 = 10[5] (i.e. written in base 5) and 6! = 720 = 625 + 75 + 20 = 10340[5] is the smallest factorial to start with digits "10" when written in base 5.

Cf. A155891--A155894, A018799, A076219.

A155895(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=5)); k}

cp's OEIS Frontend

A279089 Record values of A018799 (Smallest nonnegative integer m such that m! begins with n in base 10).

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A279090 Indices at which record values occur in A018799 (Smallest nonnegative integer m such that m! begins with n in base 10).

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A008905 Leading digit of n!.

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A076219 Smallest positive integer m such that m! begins with n in base 10.

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A155891 Least positive integer such that a(n)! starts with n, both written in binary.

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C

PARI

A155892 Least positive integer such that a(n)! starts with n, both written in base 3.

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PARI

A155894 Least positive integer such that a(n)! starts with n, both written in base 16.

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C

PARI

A018854 Smallest factorial that begins with n.

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A155893 Least positive integer such that a(n)! starts with n, both written in base 8.

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PARI

A155895 Least positive integer such that a(n)! starts with n, both written in base 5.

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