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 11-16 of 16 results.

A263450 Smallest integer k>0 such that there is at least one zero in the decimal representation of prime(n)^k.

Original entry on oeis.org

10, 10, 8, 4, 5, 6, 7, 4, 6, 4, 6, 3, 5, 3, 2, 2, 3, 5, 3, 2, 3, 3, 5, 3, 2, 1, 1, 1, 1, 4, 3, 3, 6, 4, 2, 2, 4, 3, 5, 4, 2, 4, 4, 3, 2, 2, 5, 3, 3, 3, 6, 4, 2, 2, 2, 4, 3, 3, 5, 3, 2, 4, 1, 3, 3, 2, 2, 6, 2, 2, 2, 4, 3, 5, 4, 6, 4, 2, 1, 1, 3, 4, 3, 5, 3, 3, 2, 2, 5
Offset: 1

Views

Author

Zak Seidov, Oct 18 2015

Keywords

Comments

Conjecture: there are an infinite number of ones in the sequence.
Corresponding values of prime(n)^k: 1024, 59049, 390625, 2401, 161051, 4826809, 410338673, 130321 (not yet in OEIS).
From Robert Israel, Oct 19 2015: (Start)
By Dirichlet's theorem there are infinitely many n for which prime(n) == 1 (mod 100), and these all have a(n) = 1.
All a(n) <= 20, since every x coprime to 10 has x^20 == 1 (mod 100). (End)

Links

Crossrefs

Cf. A062584, A071531, A103662, A103663.

Programs

  • Maple
    f:= proc(m) local k;
for k from 1 do
     if has(convert(m^k,base,10),0) then return k fi
   od
end proc:
seq(f(ithprime(i)), i=1..1000); # Robert Israel, Oct 19 2015
  • Mathematica
    Reap[Do[p=Prime[n];k=1;While[Min[IntegerDigits[p^k]]>0,k++];Sow[k],{n,1,200}]][[2,1]]
  • PARI
    a(n) = {p = prime(n); k = 1; while (vecmin(digits(p^k)), k++); k;} \\ Michel Marcus, Oct 21 2015

Formula

a(n) = A071531(prime(n)). - Michel Marcus, Oct 21 2015

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]}
Previous Showing 11-16 of 16 results.

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