OFFSET
1,3
COMMENTS
From Jonathan Vos Post, Jul 20 2005: (Start)
Equivalently, numbers n such that 10^n is the product of two integers without any zero digits.
10^0 = 1 * 1
10^1 = 2 * 5
10^2 = 4 * 25
10^3 = 8 * 125
10^4 = 16 * 625
10^5 = 32 * 3125
10^6 = 64 * 15625
10^7 = 128 * 78125
10^9 = 512 * 1953125
10^18 = 262144 * 3814697265625
10^33 = 8589934592 * 116415321826934814453125. (End)
Searched for n up to 10^10. - David Radcliffe, Dec 27 2015
REFERENCES
J. S. Madachy, Madachy's Mathematical Recreation, "#2. Number Toughies", pp. 126-8, Dover NY 1979.
C. S. Ogilvy and J. T. Anderson, Excursions in Number Theory. Oxford Univ. Press, 1966, p. 89.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Leroy C. Dalton & Henry D. Snyder, Topics for Mathematics Clubs, pp. 68-69, NCTM Reston VA 1983.
C. S. Ogilvy and J. T. Anderson, Excursions in Number Theory, Oxford Univ. Press, 1966, p. 89. (Annotated scanned copy).
W. Schneider, NoZeros: Powers n^k without Digit Zero [Cached copy]
MAPLE
q:= n-> andmap(t-> not 0 in convert(t, base, 10), [2^n, 5^n]):
select(q, [$0..40])[]; # Alois P. Heinz, Feb 03 2022
MATHEMATICA
Range@(10^5) // Select[Last@DigitCount@(5^#) == 0 &] // Select[Last@DigitCount@(2^#) == 0 &] (* Hans Rudolf Widmer, Feb 02 2022 *)
PROG
(PARI) isok(n) = vecmin(digits(2^n)) && vecmin(digits(5^n)); \\ Michel Marcus, Dec 28 2015
CROSSREFS
KEYWORD
fini,nonn,full,base
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Oct 24 2009 at the suggestion of M. F. Hasler
STATUS
approved