A033921 -id:A033921 - cp's OEIS frontend

A046287 Numbers k such that 2^k contains 2^1=2 as its largest proper substring of the form 2^m (probably finite).

5, 8, 9, 17, 21

Offset: 1

Patrick De Geest, Jun 15 1998

A046291 Numbers k such that 2^k contains 2^5=32 as its largest proper substring of the form 2^m.

15, 25, 41, 45, 47, 65, 71, 73, 76, 82, 85, 95, 97, 100, 110, 112, 118, 120, 132, 137, 143, 145, 147, 151, 154, 156, 158, 160, 162, 164, 170, 179, 180, 185, 195, 196, 201, 214, 216, 219, 225, 227, 233, 235, 238, 251, 252, 275, 284, 290, 295, 297, 301, 304

Offset: 1

Patrick De Geest, Jun 15 1998

If there is a term beyond a(108)=1862 it is larger than 10^5. - Giovanni Resta, Oct 14 2019

			2^15 = {32}768;
2^25 = 335544{32};
2^41 = 219902{32}55552.

Giovanni Resta, Table of n, a(n) for n = 1..108

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[2000], sub2[#] == 5 &] (* Giovanni Resta, Oct 14 2019 *)

A046292 Numbers k such that 2^k contains 2^6=64 as its largest proper substring of the form 2^m.

Original entry on oeis.org

26, 31, 46, 59, 66, 67, 72, 77, 83, 86, 89, 92, 96, 101, 106, 111, 116, 119, 123, 124, 125, 126, 129, 131, 136, 138, 141, 142, 144, 148, 152, 153, 155, 157, 163, 165, 166, 171, 176, 177, 178, 181, 182, 183, 186, 193, 194, 197, 198, 199, 202, 204, 205, 206

Offset: 1

Patrick De Geest, Jun 15 1998

If there is a term beyond a(747) = 7954, it is larger than 250000. - Giovanni Resta, Oct 14 2019

			2^26 = 671088{64};
2^31 = 2147483{64}8;
2^46 = 703687441776{64}.

Giovanni Resta, Table of n, a(n) for n = 1..747

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[300], sub2[#] == 6 &] (* Giovanni Resta, Oct 14 2019 *)

A046296 Numbers k such that 2^k contains 2^10 = 1024 as its largest proper substring of the form 2^m.

Original entry on oeis.org

224, 278, 286, 473, 502, 510, 645, 656, 698, 744, 871, 889, 909, 921, 955, 960, 966, 972, 1010, 1062, 1086, 1113, 1163, 1182, 1200, 1201, 1208, 1271, 1273, 1282, 1315, 1327, 1377, 1431, 1444, 1510, 1541, 1550, 1564, 1570, 1583, 1610, 1626, 1674, 1677

Offset: 1

Patrick De Geest, Jun 15 1998

Cf. A000079, A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[1677], sub2[#] == 10 &] (* Giovanni Resta, Oct 14 2019 *)

A046299 Numbers k such that 2^k contains 2^13=8192 as its largest proper substring of the form 2^m.

Original entry on oeis.org

105, 269, 406, 463, 505, 513, 518, 536, 559, 570, 659, 821, 924, 948, 981, 993, 995, 1013, 1081, 1133, 1136, 1165, 1199, 1246, 1279, 1281, 1312, 1330, 1331, 1344, 1354, 1362, 1363, 1408, 1434, 1436, 1447, 1454, 1480, 1488, 1491, 1499, 1501, 1503, 1513

Offset: 1

Patrick De Geest, Jun 15 1998

			2^105 = 40564{8192}07303340847894502572032.

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[ s, ToString[2^k]], k--]; k]; Select[Range[1513], sub2[#] == 13 &] (* Giovanni Resta, Oct 14 2019 *)

Definition and offset changed by M. F. Hasler, Oct 11 2019

A046300 Smallest integer k such that 2^n is the largest power of two that is contained in 2^k as a proper substring.

Original entry on oeis.org

4, 5, 6, 7, 14, 15, 26, 102, 108, 109, 224, 103, 104, 105, 506, 507, 452, 1169, 1170, 1171, 8228, 10419, 15186, 5227, 16619, 16620, 16621, 25102, 130090, 62640, 330791, 330792, 351403, 273100, 681504, 649069, 352375, 3045104, 3045105, 3635007

Offset: 0

Patrick De Geest, Jun 15 1998

First terms of A046287-A046299.

			2^4={1}6 and 2^0=1; 2^5=3{2} and 2^1=2; 2^6=6{4} and 2^2=4; etc.

Cf. A033921.

Definition reworded, offset changed to 0, and terms a(20)-a(36) added by Jon E. Schoenfield, Jun 04 2010

a(37)-a(39) from Jon E. Schoenfield, Jul 10 2010

A046288 Numbers k such that 2^k contains 2^2=4 as its largest proper substring of the form 2^m (probably finite).

Original entry on oeis.org

6, 10, 12, 18, 22, 32, 49, 52, 53, 56, 78

Offset: 1

Patrick De Geest, Jun 15 1998

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[1000], sub2[#] == 2 &] (* Giovanni Resta, Oct 14 2019 *)

A046289 Numbers k such that 2^k contains 2^3=8 as its largest proper substring of the form 2^m (probably finite).

Original entry on oeis.org

7, 11, 13, 19, 20, 23, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 42, 43, 48, 50, 51, 54, 55, 57, 58, 60, 61, 63, 68, 69, 74, 79, 80, 87, 88, 90, 91, 93, 94, 113, 115, 121, 128, 130, 139, 149, 150, 168, 169, 172, 173, 174, 187, 229, 337, 338, 376, 417

Offset: 1

Patrick De Geest, Jun 15 1998

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[500], sub2[#] == 3 &] (* Giovanni Resta, Oct 14 2019 *)

A046290 Numbers k such that 2^k contains 2^4=16 as its largest proper substring of the form 2^m (probably finite).

Original entry on oeis.org

14, 24, 40, 44, 62, 64, 70, 75, 81, 84, 98, 99, 114, 117, 122, 127, 133, 134, 140, 159, 167, 175, 184, 188, 189, 190, 200, 212, 215, 232, 234, 273, 274, 282, 292, 300, 318, 348, 377, 440, 516, 527, 620

Offset: 1

Patrick De Geest, Jun 15 1998

			2^14 = {16}384;
2^24 = {16}7772{16};
2^40 = 109951{16}27776.

Cf. A033921.

sub2[n_] := Block[{s = ToString[2^n], k = n - 1}, While[k >= 0 && ! StringContainsQ[s, ToString[2^k]], k--]; k]; Select[Range[2000], sub2[#] == 4 &] (* Giovanni Resta, Oct 14 2019 *)

A046293 Numbers k such that 2^k contains 2^7=128 as its largest proper substring of the form 2^m.

Original entry on oeis.org

102, 107, 203, 207, 248, 257, 263, 271, 307, 312, 321, 324, 329, 331, 343, 357, 362, 385, 390, 429, 458, 469, 486, 491, 524, 535, 546, 553, 568, 569, 586, 607, 614, 625, 627, 633, 634, 640, 648, 651, 662, 665, 668, 675, 688, 695, 702, 707, 711, 712, 715

Offset: 1

Patrick De Geest, Jun 15 1998

			2^102 = 50706024009129176059868{128}21504.

Cf. A033921.

cp's OEIS Frontend

A046287 Numbers k such that 2^k contains 2^1=2 as its largest proper substring of the form 2^m (probably finite).

Views

Author

Keywords

Crossrefs

A046291 Numbers k such that 2^k contains 2^5=32 as its largest proper substring of the form 2^m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A046292 Numbers k such that 2^k contains 2^6=64 as its largest proper substring of the form 2^m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A046296 Numbers k such that 2^k contains 2^10 = 1024 as its largest proper substring of the form 2^m.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A046299 Numbers k such that 2^k contains 2^13=8192 as its largest proper substring of the form 2^m.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

A046300 Smallest integer k such that 2^n is the largest power of two that is contained in 2^k as a proper substring.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A046288 Numbers k such that 2^k contains 2^2=4 as its largest proper substring of the form 2^m (probably finite).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A046289 Numbers k such that 2^k contains 2^3=8 as its largest proper substring of the form 2^m (probably finite).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A046290 Numbers k such that 2^k contains 2^4=16 as its largest proper substring of the form 2^m (probably finite).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A046293 Numbers k such that 2^k contains 2^7=128 as its largest proper substring of the form 2^m.

Views

Author

Keywords

Examples

Crossrefs