A055643 -id:A055643 - cp's OEIS frontend

A254335 Powers of 5 in base 60, concatenating the decimal values of the sexagesimal digits.

1, 5, 25, 205, 1025, 5205, 42025, 214205, 1483025, 9023205, 45124025, 346032205, 1850165025, 13411241205, 75057010025, 391445050205, 3161345251025, 16210847055205, 121454355292025, 648483937264205, 3404031807133025, 25020163036073205, 141141223300374025, 1105826524503082205, 5545214234515415025

Offset: 0

Michael De Vlieger, Jan 28 2015

Each sexagesimal digit appears as a pair of decimal digits as on a digital clock. Any leading zeros are truncated. Thus decimal 125 appears as "205" and not "0205".

			a(4) = 1025, since 5^4 = 625 = 10 * 60^1 + 25, thus 10:25 in clock-like notation, which becomes 1025 when restricted to numeric characters.

Michael De Vlieger, Table of n, a(n) for n = 0..1200

Cf. A000351 (Powers of 5), A055643 (Babylonian numbers).

Cf. Sexagesimal representations: A250073 (Powers of 2), A254334 (Powers of 3), A254336 (Powers of 10).

f[n_] := FromDigits@ StringJoin[If[# < 10, StringJoin["0", ToString[#]],
ToString[#]] & /@ IntegerDigits[5^n, 60]]; Table[f@ i, {i, 0, 24}] (* Michael De Vlieger, Jan 28 2015 *)

a(n) = subst(Pol(digits(5^n, 60)), x, 100); \\ Michel Marcus, Feb 22 2015

a(n) = A055643(A000351(n)). - Michel Marcus, Mar 02 2015

A254336 Powers of 10 in base 60, concatenating the decimal values of the sexagesimal digits.

Original entry on oeis.org

1, 10, 140, 1640, 24640, 274640, 4374640, 46174640, 742574640, 11709374640, 125136174640, 2083602574640, 21260029374640, 334200456174640, 3543204922574640, 55713281349374640, 593214421816174640, 9552227030242574640, 139134430302709374640, 1632172505043136174640, 24522541050451602574640

Offset: 0

Michael De Vlieger, Jan 28 2015

Each sexagesimal digit appears as a pair of decimal digits as on a digital clock. Any leading zeros are truncated. Thus decimal 100 appears as "140" and not "0140".

			a(3) = 1640, since 10^3 = 1000 = 16 * 60^1 + 40, thus 16:40 in clock-like notation, which becomes 1640 when restricted to numeric characters.

Michael De Vlieger, Table of n, a(n) for n = 0..600

Cf. A011557 (Powers of 10), A055643 (Babylonian numbers).

Cf. Sexagesimal representations: A250073 (Powers of 2), A254334 (Powers of 3), A254335 (Powers of 5).

f[n_] := FromDigits@ StringJoin[If[# < 10, StringJoin["0", ToString[#]],
ToString[#]] & /@ IntegerDigits[10^n, 60]]; Table[f@ i, {i, 0, 20}] (* Michael De Vlieger, Jan 28 2015 *)

a(n) = subst(Pol(digits(10^n, 60)), x, 100); \\ Michel Marcus, Feb 22 2015

a(n) = A055643(A011557(n)). - Michel Marcus, Mar 02 2015

A091722 Babylonian sexagesimal (base 60) expansion of 1/13.

Original entry on oeis.org

4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55, 23, 4, 36, 55

Offset: 0

Jeppe Stig Nielsen, Feb 01 2004

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1).

Cf. A021017, A091721, A091722, A055643.

Cf. A159991. - Reinhard Zumkeller, May 02 2009

RealDigits[ 1/13, 60, 75] [[1]] (* Robert G. Wilson v, Feb 02 2004 *)

A281863 Alternating powers of 60 and 10 times powers of 60.

Original entry on oeis.org

1, 10, 60, 600, 3600, 36000, 216000, 2160000, 12960000, 129600000, 777600000, 7776000000, 46656000000, 466560000000, 2799360000000, 27993600000000, 167961600000000, 1679616000000000, 10077696000000000, 100776960000000000, 604661760000000000

Offset: 0

Wolfdieter Lang, Feb 19 2017

These numbers are the values for the positions in the Sumerian (and Babylonian) alternating sexagesimal - decimal system (used at least up to 10*60^2 = 36000, but here extended).

For the numbers in this mixed base system see A055643. For the number of symbols needed for representing n see A131650. For the number of digits (including 0) of the representation of n see A282622.

Georges Ifrah, Histoire Universelle des Chiffres, Paris, 1981.
Georges Ifrah, From one to zero, A universal history of numbers, Viking Penguin Inc., 1985.
Georges Ifrah, Universalgeschichte der Zahlen, Campus Verlag, Frankfurt, New York, 2. Auflage, 1987, pp. 210-221.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 127.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,60).

Cf. A131650, A055643, A282622.

LinearRecurrence[{0,60},{1,10},21] (* or *) a[0]=1;a[1]=10;a[n_]:=60*a[n-2];Table[a[n],{n,0,20}] (* Indranil Ghosh, Feb 21 2017 *)

Vec((1 + 10*x) / (1 - 60*x^2) + O(x^30)) \\ Colin Barker, Feb 21 2017

a(2*n) = 60^(n/2), a(2*n+1) = 10*60^((n-1)/2), n >= 0.
From Colin Barker, Feb 21 2017: (Start)
a(n) = 60*a(n-2) for n>1.
G.f.: (1 + 10*x) / (1 - 60*x^2). (End)
E.g.f.: cosh(2*sqrt(15)*x) + sqrt(5/3)*sinh(2*sqrt(15)*x). - Stefano Spezia, Sep 08 2024

A357996 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A006942).

Original entry on oeis.org

1, 2, 4, 14, 25, 37, 70, 105, 123, 153, 186, 182, 156, 139, 119, 79, 35, 9, 1

Offset: 8

Stefano Spezia, Oct 23 2022

Since 8 <= A357970(n) <= 26 the sequence is finite and begins with offset 8.

Index entries for sequences related to calculator display

Histogram of A357970.
Cf. A006942, A008588, A055642, A055643.
Variants: A357997, A357998, A357999, A358000.

a055643[n_]:=FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[n, 60]]; a006942[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 6}); a[n_]:=a006942[a055643[n]]+6(4-Ceiling[Log10[a055643[n]+1]]); Table[Count[Join[{24},Array[a,1439]],n],{n,8,26}]

A357997 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A010371).

Original entry on oeis.org

1, 0, 5, 10, 16, 35, 66, 88, 119, 166, 187, 177, 161, 154, 129, 81, 35, 9, 1

Offset: 8

Stefano Spezia, Oct 23 2022

Since 8 <= A357971(n) <= 26 the sequence is finite and begins with offset 8.

Index entries for sequences related to calculator display

Histogram of A357971.
Cf. A008588, A010371, A055642, A055643.
Variants: A357996, A357998, A357999, A358000.

a055643[n_]:=FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[n, 60]]; a010371[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 4, 8 -> 7, 9 -> 6}); a[n_]:=a010371[a055643[n]]+6(4-Ceiling[Log10[a055643[n]+1]]); Table[Count[Join[{24},Array[a,1439]],n],{n,8,26}]

A357998 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A063720).

Original entry on oeis.org

1, 2, 4, 18, 25, 41, 96, 103, 133, 189, 188, 154, 158, 155, 95, 53, 19, 5, 1

Offset: 8

Stefano Spezia, Oct 23 2022

Since 8 <= A357972(n) <= 26 the sequence is finite and begins with offset 8.

Index entries for sequences related to calculator display

Histogram of A357972.
Cf. A008588, A055642, A055643, A063720.
Variants: A357996, A357997, A357999, A358000.

a055643[n_]:=FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[n, 60]]; a063720[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 6 -> 5, 7 -> 3, 8 -> 7, 9 -> 5}); a[n_]:=a063720[a055643[n]]+6(4-Ceiling[Log10[a055643[n]+1]]);Table[Count[Join[{24},Array[a,1439]],n],{n,8,26}]

A357999 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A074458).

Original entry on oeis.org

1, 0, 5, 12, 14, 41, 74, 87, 128, 185, 185, 162, 167, 159, 119, 67, 26, 7, 1

Offset: 8

Stefano Spezia, Oct 23 2022

Since 8 <= A357973(n) <= 26 the sequence is finite and begins with offset 8.

Index entries for sequences related to calculator display

Histogram of A357973.
Cf. A008588, A055642, A055643, A074458.
Variants: A357996, A357997, A357998, A358000.

a055643[n_]:=FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[n, 60]]; a074458[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 4, 8 -> 7, 9 -> 5}); a[n_]:=a074458[a055643[n]]+6(4-Ceiling[Log10[a055643[n]+1]]);Table[Count[Join[{24},Array[a,1439]],n],{n,8,26}]

A358000 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A277116).

Original entry on oeis.org

1, 2, 4, 16, 25, 39, 82, 106, 126, 170, 190, 169, 154, 146, 111, 65, 26, 7, 1

Offset: 8

Stefano Spezia, Oct 23 2022

Since 8 <= A357974(n) <= 26 the sequence is finite and begins with offset 8.

Index entries for sequences related to calculator display

Histogram of A357974.
Cf. A008588, A055642, A055643, A277116.
Variants: A357996, A357997, A357998, A357999.

a055643[n_]:=FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[n, 60]]; a277116[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 5}); a[n_]:=a277116[a055643[n]]+6(4-Ceiling[Log10[a055643[n]+1]]);Table[Count[Join[{24},Array[a,1439]],n],{n,8,26}]

A091721 Babylonian sexagesimal (base 60) expansion of 1/11.

Original entry on oeis.org

5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21, 49, 5, 27, 16, 21

Offset: 0

Jeppe Stig Nielsen, Feb 01 2004

Period 5: repeat [5, 27, 16, 21, 49]. - Wesley Ivan Hurt, May 25 2024

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 1).

Cf. A092291, A091720, A091722, A055643.

Cf. A159991. - Reinhard Zumkeller, May 02 2009

RealDigits[ 1/11, 60, 75] [[1]] (* Robert G. Wilson v, Feb 02 2004 *)
CoefficientList[Series[(5 + 27 x + 16 x^2 + 21 x^3 + 49 x^4)/(1 - x^5), {x, 0, 40}], x] (* Wesley Ivan Hurt, May 25 2024 *)

From Wesley Ivan Hurt, May 25 2024: (Start)
a(n+5) = a(n).
G.f.: (5+27*x+16*x^2+21*x^3+49*x^4)/(1-x^5). (End)

cp's OEIS Frontend

A254335 Powers of 5 in base 60, concatenating the decimal values of the sexagesimal digits.

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A254336 Powers of 10 in base 60, concatenating the decimal values of the sexagesimal digits.

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A091722 Babylonian sexagesimal (base 60) expansion of 1/13.

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A281863 Alternating powers of 60 and 10 times powers of 60.

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A357996 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A006942).

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A357997 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A010371).

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Mathematica

A357998 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A063720).

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Mathematica

A357999 a(n) is the number of times in the format hh:mm that can be represented in a 7-segment display by using only n segments (version A074458).

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