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A306117 Largest k such that 7^k has exactly n digits 0 (in base 10), conjectured. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
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.)
PROG
(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]}
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.
Sequence in context: A248659 A089268 A214469 * A039418 A043241 A044021
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jun 22 2018
STATUS
approved

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Last modified July 23 11:07 EDT 2024. Contains 374549 sequences. (Running on oeis4.)