A067480 -id:A067480 - cp's OEIS frontend

A320860 Powers of 2 with initial digit 4.

4, 4096, 4194304, 4294967296, 4398046511104, 4503599627370496, 4611686018427387904, 4722366482869645213696, 4835703278458516698824704, 4951760157141521099596496896, 40564819207303340847894502572032, 41538374868278621028243970633760768

Offset: 1

Muniru A Asiru, Oct 22 2018

Differs from A067482 first at n = 11.

Muniru A Asiru, Table of n, a(n) for n = 1..320
Index to divisibility sequences

Cf. A000079 (Powers of 2), A008952 (leading digit of 2^n), A217397 (numbers starting with 4).

Powers of 2 with initial digit k, (k = 1..4): A067488, A067480, A320859, this sequence.

Filtered(List([0..150],n->2^n),i->ListOfDigits(i)[1]=4);

[2^n: n in [1..160] | Intseq(2^n)[#Intseq(2^n)] eq 4]; // G. C. Greubel, Oct 27 2018

select(x->"4"=""||x[1],[2^n$n=0..150])[];

Select[2^Range[160], First[IntegerDigits[#]] == 4 &] (* G. C. Greubel, Oct 27 2018 *)

select(x->(digits(x)[1]==4), vector(200, n, 2^n)) \\ Michel Marcus, Oct 26 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

A320861 Powers of 2 with initial digit 5.

Original entry on oeis.org

512, 524288, 536870912, 549755813888, 562949953421312, 576460752303423488, 590295810358705651712, 5070602400912917605986812821504, 5192296858534827628530496329220096, 5316911983139663491615228241121378304, 5444517870735015415413993718908291383296

Offset: 1

Muniru A Asiru, Oct 23 2018

Robert Israel, Table of n, a(n) for n = 1..263
Index to divisibility sequences

Cf. A000079 (powers of 2), A008952 (leading digit of 2^n).

Powers of 2 with initial digit k, (k = 1..5): A067488, A067480, A320859, A320860, this sequence.

Filtered(List([0..160],n->2^n),i->ListOfDigits(i)[1]=5);

[2^n: n in [1..200] | Intseq(2^n)[#Intseq(2^n)] eq 5]; // Vincenzo Librandi, Oct 25 2018

select(x->"5"=""||x[1],[2^n$n=0..160])[];
# Alternative:
Res:= NULL: count:= 0:
for k from 1 to 49 do
   n:= ilog2(6*10^k);
   if n > ilog2(5*10^k) then count:= count+1;
     Res:= Res, 2^n;
   fi
od:
Res; # Robert Israel, Oct 26 2018

Select[2^Range[200], First[IntegerDigits[#]]==5 &] (* Vincenzo Librandi, Oct 25 2018 *)

lista(nn) = {for(n=1, nn, x = 2^n; if (digits(x=2^n)[1] == 5, print1(x, ", ")););} \\ Michel Marcus, Oct 25 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

A320862 Powers of 2 with initial digit 6.

Original entry on oeis.org

64, 65536, 67108864, 68719476736, 604462909807314587353088, 618970019642690137449562112, 633825300114114700748351602688, 649037107316853453566312041152512, 664613997892457936451903530140172288, 680564733841876926926749214863536422912

Offset: 1

Muniru A Asiru, Oct 23 2018

Muniru A Asiru, Table of n, a(n) for n = 1..220
Index to divisibility sequences

Cf. A000079 (powers of 2), A008952 (leading digit of 2^n), A217399 (numbers starting with 6).

Powers of 2 with initial digit k, (k = 1..6): A067488, A067480, A320859, A320860, A320861, this sequence.

Filtered(List([0..180],n->2^n),i->ListOfDigits(i)[1]=6);

[2^n: n in [1..160] | Intseq(2^n)[#Intseq(2^n)] eq 6]; // G. C. Greubel, Oct 27 2018

select(x->"6"=""||x[1],[2^n$n=0..180])[];

Select[2^Range[160], First[IntegerDigits[#]] == 6 &] (* G. C. Greubel, Oct 27 2018 *)

select(x->(digits(x)[1]==6), vector(200, n, 2^n)) \\ Michel Marcus, Oct 26 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

A320863 Powers of 2 with initial digit 7.

Original entry on oeis.org

70368744177664, 72057594037927936, 73786976294838206464, 75557863725914323419136, 77371252455336267181195264, 79228162514264337593543950336, 713623846352979940529142984724747568191373312, 730750818665451459101842416358141509827966271488

Offset: 1

Muniru A Asiru, Oct 26 2018

Muniru A Asiru, Table of n, a(n) for n = 1..170
Index to divisibility sequences

Cf. A000079 (powers of 2), A008952 (leading digit of 2^n), A217400 (numbers starting with 7).

Powers of 2 with initial digit k, (k = 1..7): A067488, A067480, A320859, A320860, A320861, A320862, this sequence.

Filtered(List([0..180],n->2^n),i->ListOfDigits(i)[1]=7);

[2^n: n in [1..160] | Intseq(2^n)[#Intseq(2^n)] eq 7]; // G. C. Greubel, Oct 27 2018

select(x->"7"=""||x[1],[2^n$n=0..180])[];

Select[2^Range[160], First[IntegerDigits[#]] == 7 &] (* G. C. Greubel, Oct 27 2018 *)

select(x->(digits(x)[1]==7), vector(200, n, 2^n)) \\ Michel Marcus, Oct 27 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

A320864 Powers of 2 with initial digit 8.

Original entry on oeis.org

8, 8192, 8388608, 8589934592, 8796093022208, 81129638414606681695789005144064, 83076749736557242056487941267521536, 85070591730234615865843651857942052864, 87112285931760246646623899502532662132736, 89202980794122492566142873090593446023921664

Offset: 1

Muniru A Asiru, Nov 21 2018

Muniru A Asiru, Table of n, a(n) for n = 1..170
Index to divisibility sequences

Cf. A000079 (powers of 2), A008952 (leading digit of 2^n), A217401 (numbers starting with 8).

Powers of 2 with initial digit k, (k = 1..8): A067488, A067480, A320859, A320860, A320861, A320862, A320863, this sequence.

Filtered(List([0..200],n->2^n),i->ListOfDigits(i)[1]=8);

select(x->"8"=""||x[1],[2^n$n=0..200])[];

Select[2^Range[200], IntegerDigits[#][[1]] == 8 &] (* Amiram Eldar, Nov 21 2018 *)

select(x->(digits(x)[1]==8), vector(200, n, 2^n)) \\ Michel Marcus, Nov 21 2018

cp's OEIS Frontend

A320860 Powers of 2 with initial digit 4.

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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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A320861 Powers of 2 with initial digit 5.

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A067492 Powers of 6 with initial digit 1.

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A320862 Powers of 2 with initial digit 6.

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A067493 Powers of 7 with initial digit 1.

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A320863 Powers of 2 with initial digit 7.

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