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

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

0,1

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

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) 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]}

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.

Sequence in context: A130694 A269748 A153831 * A058980 A079703 A281235

Adjacent sequences: A306110 A306111 A306112 * A306114 A306115 A306116

Keyword

nonn,base

Author

M. F. Hasler, Jun 22 2018

Status

approved