|
|
A306113
|
|
Largest k such that 3^k has exactly n digits 0 (in base 10), conjectured.
|
|
0
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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 }.
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|