A007496 Numbers n such that the decimal expansions of 2^n and 5^n contain no 0's (probably 33 is last term). (Formerly M0497)

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

Offset

1,3

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

Table of n, a(n) for n=1..11.

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]

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

Cf. A007377, A008839.

Sequence in context: A048319 A037405 A048333 * A082274 A029804 A084690

Adjacent sequences: A007493 A007494 A007495 * A007497 A007498 A007499

Keyword

fini,nonn,full,base

Author

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

Extensions

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

Status

approved