cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-27 of 27 results.

A306113 Largest k such that 3^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

68, 73, 136, 129, 205, 237, 317, 268, 251, 276, 343, 372, 389, 419, 565, 416, 494, 571, 637, 628, 713, 629, 638, 655, 735, 690, 862, 802, 750, 863, 826, 996, 976, 1008, 1085, 1026, 1130, 995, 962, 1082, 1136, 1064, 1176, 1084, 1215, 1354, 1298, 1275, 1226, 1468, 1353
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A030700: exponents of powers of 3 without digit 0.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063555: least k such that 3^k has n digits 0 in base 10.
Cf. A305943: number of k's such that 3^k has n digits 0.
Cf. A305933: row n lists exponents of 3^k with n digits 0.
Cf. A030700: { k | 3^k has no digit 0 } : row 0 of the above.
Cf. A238939: { 3^k having no digit 0 }.
Cf. A305930: number of 0's in 3^n.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306113_vec(nMax,M=99*nMax+199,x=3,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A306114 Largest k such that 4^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

43, 92, 77, 88, 115, 171, 182, 238, 235, 308, 324, 348, 412, 317, 366, 445, 320, 424, 362, 448, 546, 423, 540, 545, 612, 605, 567, 571, 620, 641, 619, 700, 708, 704, 808, 762, 811, 744, 755, 971, 896, 900, 935, 862, 986, 954, 982, 956, 1057, 1037, 1128
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A030701: exponents of powers of 4 without digit 0 in base 10.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063575: least k such that 4^k has n digits 0 in base 10.
Cf. A305944: number of k's such that 4^k has n digits 0.
Cf. A305924: row n lists exponents of 4^k with n digits 0.
Cf. A030701: { k | 4^k has no digit 0 } : row 0 of the above.
Cf. A238940: { 4^k having no digit 0 }.
Cf. A020665: largest k such that n^k has no digit 0 in base 10.
Cf. A071531: least k such that n^k contains a digit 0 in base 10.
Cf. A103663: least x such that x^n has no digit 0 in base 10.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306114_vec(nMax,M=99*nMax+199,x=4,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A306115 Largest k such that 5^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

58, 85, 107, 112, 127, 157, 155, 194, 198, 238, 323, 237, 218, 301, 303, 324, 339, 476, 321, 284, 496, 421, 475, 415, 537, 447, 494, 538, 531, 439, 473, 546, 587, 588, 642, 690, 769, 689, 687, 686, 757, 732, 683, 826, 733, 825, 833, 810, 827, 888, 966
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A008839: exponents of powers of 5 without digit 0 in base 10.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063585: least k such that 5^k has n digits 0 in base 10.
Cf. A305945: number of k's such that 5^k has n digits 0.
Cf. A305925: row n lists exponents of 5^k with n digits 0.
Cf. A008839: { k | 5^k has no digit 0 } : row 0 of the above.
Cf. A195948: { 5^k having no digit 0 }.
Cf. A020665: largest k such that n^k has no digit 0 in base 10.
Cf. A071531: least k such that n^k contains a digit 0 in base 10.
Cf. A103663: least x such that x^n has no digit 0 in base 10.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306115_vec(nMax,M=99*nMax+199,x=5,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A306116 Largest k such that 6^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

44, 59, 63, 82, 98, 134, 108, 123, 199, 189, 192, 200, 275, 282, 267, 307, 298, 296, 391, 338, 340, 396, 328, 436, 432, 478, 484, 615, 428, 529, 492, 515, 536, 523, 627, 665, 559, 592, 637, 560, 654, 674, 590, 653, 728, 791, 753, 781, 812, 783, 788
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A030702: exponents of powers of 6 without digit 0 in base 10.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063596: least k such that 6^k has n digits 0 in base 10.
Cf. A305946: number of k's such that 6^k has n digits 0.
Cf. A305926: row n lists exponents of 6^k with n digits 0.
Cf. A030702: { k | 6^k has no digit 0 } : row 0 of the above.
Cf. A238936: { 6^k having no digit 0 }.
Cf. A020665: largest k such that n^k has no digit 0 in base 10.
Cf. A071531: least k such that n^k contains a digit 0 in base 10.
Cf. A103663: least x such that x^n has no digit 0 in base 10.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306116_vec(nMax,M=99*nMax+199,x=6,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A306117 Largest k such that 7^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

35, 51, 93, 58, 122, 74, 108, 131, 118, 152, 195, 192, 236, 184, 247, 243, 254, 286, 325, 292, 318, 336, 375, 393, 339, 431, 327, 433, 485, 447, 456, 455, 448, 492, 452, 507, 489, 541, 526, 605, 627, 706, 730, 628, 665, 660, 798, 715, 704, 633, 728
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A030703: exponents of powers of 7 without digit 0 in base 10.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063606: least k such that 7^k has n digits 0 in base 10.
Cf. A305947: number of k's such that 7^k has n digits 0.
Cf. A305927: row n lists exponents of 6^k with n digits 0.
Cf. A030703: { k | 7^k has no digit 0 } : row 0 of the above.
Cf. A195908: { 7^k having no digit 0 }.
Cf. A020665: largest k such that n^k has no digit 0 in base 10.
Cf. A071531: least k such that n^k contains a digit 0 in base 10.
Cf. A103663: least x such that x^n has no digit 0 in base 10.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306117_vec(nMax,M=99*nMax+199,x=7,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A306118 Largest k such that 8^k has exactly n digits 0 (in base 10), conjectured.

Original entry on oeis.org

27, 43, 77, 61, 69, 119, 115, 158, 159, 168, 216, 232, 202, 198, 244, 270, 229, 274, 241, 273, 364, 283, 413, 298, 408, 341, 378, 431, 404, 403, 465, 483, 472, 454, 467, 508, 540, 575, 485, 576, 511, 623, 538, 515, 560, 655, 647, 661, 648, 639, 752
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) is the largest term in A030704: exponents of powers of 8 without digit 0 in base 10.
There is no proof for any of the terms, just as for any term of A020665 and many similar / related sequences. However, the search has been pushed to many magnitudes beyond the largest known term, and the probability of any of the terms being wrong is extremely small, cf., e.g., the Khovanova link.

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, Mar 07 2014, updated 2018.
  • T. Khovanova, The 86-conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
  • W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.org--see A007496 for a cached copy.)

Crossrefs

Cf. A063616: least k such that 8^k has n digits 0 in base 10.
Cf. A305938: number of k's such that 8^k has n digits 0.
Cf. A305928: row n lists exponents of 8^k with n digits 0.
Cf. A030704: { k | 8^k has no digit 0 } : row 0 of the above.
Cf. A020665: largest k such that n^k has no digit 0 in base 10.
Cf. A071531: least k such that n^k contains a digit 0 in base 10.
Cf. A103663: least x such that x^n has no digit 0 in base 10.
Cf. A306112, ..., A306119: analog for 2^k, ..., 9^k.

Programs

  • PARI
    A306118_vec(nMax,M=99*nMax+199,x=8,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(x^k)),nMax)]=k);a[^-1]}

A152520 Numbers n such that the decimal expansion of 2^n+5^n contains no 2's and no 5's (probably 11 is the last term).

Original entry on oeis.org

1, 3, 4, 8, 10, 11
Offset: 1

Views

Author

Zak Seidov, Oct 25 2009

Keywords

Examples

			{n, 2^n+5^n}:{1,7}, {3,133}, {4,641}, {8,390881}, {10,9766649}, {11,48830173}.

Crossrefs

Cf. A074600, A007496, A152493.

Programs

  • Mathematica
    Do[If[Intersection[IntegerDigits[p=2^n+5^n],{2,5}]=={},Print[{n,p}]],{n,0,2000}]
Previous Showing 21-27 of 27 results.

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