

A306114


Largest k such that 4^k has exactly n digits 0 (in base 10), conjectured.


0



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
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OFFSET

0,1


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

Table of n, a(n) for n=0..50.
M. F. Hasler, Zeroless powers, OEIS Wiki, March 2014, updated 2018.
T. Khovanova, The 86conjecture, Tanya Khovanova's Math Blog, Feb. 2011.
W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.orgsee A007496 for a cached copy.)


PROG

(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]}


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.
Sequence in context: A288641 A141924 A122617 * A044181 A044562 A060323
Adjacent sequences: A306111 A306112 A306113 * A306115 A306116 A306117


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Jun 22 2018


STATUS

approved



