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

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

0,1

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

Table of n, a(n) for n=0..50.

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.)

Prog

(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]}

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.

Sequence in context: A231402 A116227 A214176 * A185590 A029690 A353538

Adjacent sequences: A306113 A306114 A306115 * A306117 A306118 A306119

Keyword

nonn,base

Author

M. F. Hasler, Jun 22 2018

Status

approved