

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
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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

W. Schneider, No Zeros, 2000, updated 2003. (On web.archive.orgsee 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.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



