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 11-14 of 14 results.

A245853 Powers of 12 without the digit '0' in their decimal expansion.

Original entry on oeis.org

1, 12, 144, 1728, 248832, 2985984, 429981696, 61917364224, 1283918464548864, 3833759992447475122176, 11447545997288281555215581184
Offset: 1

Views

Author

Vincenzo Librandi, Aug 04 2014

Keywords

Comments

Conjectured to be finite.

Crossrefs

Cf. Powers of k without the digit '0' in their decimal expansion: A238938 (k=2), A238939 (k=3), A238940 (k=4), A195948 (k=5), A238936 (k=6), A195908 (k=7), A245852 (k=8), A240945 (k=9), A195946 (k=11), this sequence (k=12), A195945 (k=13).

Programs

  • Magma
    [12^n: n in [0..3*10^4] | not 0 in Intseq(12^n)];
  • Mathematica
    Select[12^Range[0, 2*10^5], DigitCount[#, 10, 0]==0 &]

A305946 Number of powers of 6 having exactly n digits '0' (in base 10), conjectured.

Original entry on oeis.org

14, 10, 17, 16, 11, 14, 10, 8, 12, 19, 9, 16, 13, 11, 10, 10, 11, 10, 10, 17, 7, 15, 14, 16, 13, 22, 12, 17, 15, 17, 7, 6, 14, 22, 13, 19, 14, 12, 15, 7, 11, 14, 6, 12, 9, 12, 9, 14, 13, 15, 21
Offset: 0

Views

Author

M. F. Hasler, Jun 22 2018

Keywords

Comments

a(0) = 14 is the number of terms in A030702 and in A195948, which includes the power 6^0 = 1.
These are the row lengths of A305926. It remains an open problem to provide a proof that these rows are complete (as for all terms of A020665), but the search has been pushed to many orders of magnitude beyond the largest known term, and the probability of finding an additional term is vanishing, cf. 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. A030702 = row 0 of A305926: k such that 6^k has no 0's; A238936: these powers 6^k.
Cf. A020665: largest k such that n^k has no '0's.
Cf. A063596 = column 1 of A305926: least k such that 6^k has n digits '0' in base 10.
Cf. A305942 (analog for 2^k), ..., A305947, A305938, A305939 (analog for 9^k).

Programs

  • PARI
    A305946(n,M=99*n+199)=sum(k=0,M,#select(d->!d,digits(6^k))==n)
  • PARI
    A305946_vec(nMax,M=99*nMax+199,a=vector(nMax+=2))={for(k=0,M,a[min(1+#select(d->!d,digits(6^k)),nMax)]++);a[^-1]}

A252482 Exponents n such that the decimal expansion of the power 12^n contains no zeros.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 10, 14, 20, 26
Offset: 1

Views

Author

M. F. Hasler, Dec 17 2014

Keywords

Comments

Conjectured to be finite.
See A245853 for the actual powers 12^a(n).

Links

  • M. F. Hasler, Zeroless powers, OEIS Wiki, Mar 07 2014
  • Eric Weisstein's World of Mathematics, Zero

Crossrefs

For zeroless powers x^n, see A238938 (x=2), A238939, A238940, A195948, A238936, A195908, A245852, A240945 (k=9), A195946 (x=11), A245853, A195945; A195942, A195943, A103662.
For the corresponding exponents, see A007377, A030700, A030701, A008839, A030702, A030703, A030704, A030705, A030706, this sequence A252482, A195944.
For other related sequences, see A052382, A027870, A102483, A103663.

Programs

  • Mathematica
    Select[Range[0,30],DigitCount[12^#,10,0]==0&] (* Harvey P. Dale, Apr 06 2019 *)
  • PARI
    for(n=0,9e9,vecmin(digits(12^n))&&print1(n","))

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]}
Previous Showing 11-14 of 14 results.

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