A007496 Numbers n such that the decimal expansions of 2^n and 5^n contain no 0's (probably 33 is last term).

0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 33

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• fini
• nonn
• full
• base

Comments

Intersection of A007377 and A008839. - Lekraj Beedassy, Jul 27 2004

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.
• G. P. Michon, What two integers without zero digits have a product of 1000000000?
• 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]

Crossrefs

Cf. A007377, A008839.

Programs

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 *)

PARI

isok(n) = vecmin(digits(2^n)) && vecmin(digits(5^n)); \\ Michel Marcus, Dec 28 2015

Extensions

Edited by N. J. A. Sloane, Oct 24 2009 at the suggestion of M. F. Hasler