A067486 -id:A067486 - cp's OEIS frontend

A067488 Powers of 2 with initial digit 1.

1, 16, 128, 1024, 16384, 131072, 1048576, 16777216, 134217728, 1073741824, 17179869184, 137438953472, 1099511627776, 17592186044416, 140737488355328, 1125899906842624, 18014398509481984, 144115188075855872, 1152921504606846976, 18446744073709551616

Offset: 1

Amarnath Murthy, Feb 09 2002

Also smallest n-digit power of 2.

For each range 10^(n-1) to 10^n-1 there exists exactly 1 power of 2 with first digit 1 (floor(log_10(a(n))) = n-1). As such, the density of this sequence relative to all powers of 2 (A000079) is log(2)/log(10) (0.301..., A007524), which is prototypical of Benford's Law. - Charles L. Hohn, Jul 23 2024

Muniru A Asiru, Table of n, a(n) for n = 1..993
Index to divisibility sequences

Cf. A000079, A067497, A055642,
Other initial digits: A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A074116.
Cf. A074117, A074118.

Filtered(List([0..60],n->2^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

[2^n: n in [0..100] | Intseq(2^n)[#Intseq(2^n)] eq 1]; // Vincenzo Librandi, Dec 31 2024

Select[2^Range[0, 70], First[IntegerDigits[#]] == 1 &]  (* Harvey P. Dale, Mar 14 2011 *)

a(n)=2^ceil((n-1)*log(10)/log(2)) \\ Charles R Greathouse IV, Apr 08 2012

(List.fill(50)(2: BigInt)).scanLeft(1: BigInt)( * ).filter(.toString.startsWith("1")) // _Alonso del Arte, Jan 16 2020

a(n) = 2^ceiling((n-1)*log(10)/log(2)). - Benoit Cloitre, Aug 29 2002
From Charles L. Hohn, Jun 09 2024: (Start)
a(n) = 2^A067497(n-1).
A055642(a(n)) = n. (End)

A067487 Powers of 9 with initial digit 9.

Original entry on oeis.org

9, 984770902183611232881, 969773729787523602876821942164080815560161, 955004950796825236893190701774414011919935138974343129836853841, 940461086986004843694934910131056317906479029659199959555574885740211572136210345921

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..48

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486.

Filtered(List([0..100],n->9^n),i->ListOfDigits(i)[1]=9); # Muniru A Asiru, Oct 21 2018

[9^n: n in [1..100] | Intseq(9^n)[#Intseq(9^n)] eq 9]; // Vincenzo Librandi, Oct 22 2018

 Select[9^Range[100], First[IntegerDigits[#]]==9 &] (* Vincenzo Librandi, Oct 22 2018 *)

More terms from Benoit Cloitre, Feb 28 2002

A067489 Powers of 3 with initial digit 1.

Original entry on oeis.org

1, 19683, 177147, 1594323, 14348907, 129140163, 1162261467, 10460353203, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089, 12157665459056928801, 109418989131512359209

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..625

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488.

Filtered(List([0..50],n->3^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

Select[3^Range[0,5*10^6],First[IntegerDigits[#]]==1&] (* Harvey P. Dale, Oct 09 2015 *)

Offset 1 from Michel Marcus, Oct 19 2018

A067490 Powers of 4 with initial digit 1.

Original entry on oeis.org

1, 16, 1024, 16384, 1048576, 16777216, 1073741824, 17179869184, 1099511627776, 17592186044416, 1125899906842624, 18014398509481984, 1152921504606846976, 18446744073709551616, 1180591620717411303424, 18889465931478580854784, 1208925819614629174706176

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..400
Index to divisibility sequences

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489.

Filtered(List([0..40],n->4^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

select(x-> "1"=""||x[1],[4^n$n=0..60])[];  # Alois P. Heinz, Oct 22 2018

a(n+1)/a(n) is in {16, 64, 1024}, so 16^n <= a(n+1) < 1024^n. Asymptotically, the exponent should be 100; I can prove that 99^n << a(n) << 101^n. [Charles R Greathouse IV, Jan 19 2012]

a(16) inserted by Muniru A Asiru, Oct 22 2018

A067491 Powers of 5 with initial digit 1.

Original entry on oeis.org

1, 125, 15625, 1953125, 1220703125, 152587890625, 19073486328125, 11920928955078125, 1490116119384765625, 186264514923095703125, 116415321826934814453125, 14551915228366851806640625, 1818989403545856475830078125, 1136868377216160297393798828125

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..300

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489, A067490.

Filtered(List([0..40],n->5^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 21 2018

select(x-> "1"=""||x[1], [5^n$n=0..50])[];  # Alois P. Heinz, Oct 21 2018

Offset 1 from Michel Marcus, Oct 19 2018

A067492 Powers of 6 with initial digit 1.

Original entry on oeis.org

1, 1296, 1679616, 10077696, 13060694016, 16926659444736, 101559956668416, 131621703842267136, 170581728179578208256, 1023490369077469249536, 1326443518324400147398656, 1719070799748422591028658176

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..387

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489, A067490, A067491.

Filtered(List([0..40],n->6^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

Select[6^Range[0,40],IntegerDigits[#][[1]]==1&] (* Harvey P. Dale, Oct 04 2023 *)

Offset 1 from Michel Marcus, Oct 19 2018

A067493 Powers of 7 with initial digit 1.

Original entry on oeis.org

1, 16807, 117649, 1977326743, 13841287201, 1628413597910449, 11398895185373143, 191581231380566414401, 1341068619663964900807, 157775382034845806615042743, 1104427674243920646305299201

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..357

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489, A067490, A067491, A067492.

Filtered(List([0..40],n->7^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

Offset 1 by Michel Marcus, Oct 19 2018

A067494 Powers of 8 with initial digit 1.

Original entry on oeis.org

1, 16777216, 134217728, 1073741824, 18014398509481984, 144115188075855872, 1152921504606846976, 19342813113834066795298816, 154742504910672534362390528, 1237940039285380274899124224

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..330

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489, A067490, A067491, A067492, A067493.

Filtered(List([0..40],n->8^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

Select[8^Range[0,30],IntegerDigits[#][[1]]==1&] (* Harvey P. Dale, Jun 10 2023 *)

Offset 1 by Michel Marcus, Oct 19 2018

A067495 Powers of 9 having initial digit 1.

Original entry on oeis.org

1, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089, 12157665459056928801, 109418989131512359209, 1824800363140073127359051977856583921, 16423203268260658146231467800709255289, 147808829414345923316083210206383297601

Offset: 1

Amarnath Murthy, Feb 09 2002

Muniru A Asiru, Table of n, a(n) for n = 1..250

Cf. A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A067488, A067489, A067490, A067491, A067492, A067493, A067494.

Filtered(List([0..40],n->9^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

select(x-> "1"=""||x[1],[9^n$n=0..60])[];  # Alois P. Heinz, Oct 22 2018

Select[9^Range[0,50],First[IntegerDigits[#]]==1&] (* Harvey P. Dale, Oct 01 2015 *)

More terms from Harvey P. Dale, Oct 01 2015

cp's OEIS Frontend

A067488 Powers of 2 with initial digit 1.

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A067487 Powers of 9 with initial digit 9.

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A067489 Powers of 3 with initial digit 1.

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A067490 Powers of 4 with initial digit 1.

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A067491 Powers of 5 with initial digit 1.

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A067492 Powers of 6 with initial digit 1.

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A067493 Powers of 7 with initial digit 1.

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A067494 Powers of 8 with initial digit 1.

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