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A178483 For n=1,2,... list all products of the first n primes raised to some nonnegative power less than n. 3
1, 1, 2, 3, 6, 1, 2, 4, 3, 6, 12, 9, 18, 36, 5, 10, 20, 15, 30, 60, 45, 90, 180, 25, 50, 100, 75, 150, 300, 225, 450, 900, 1, 2, 4, 8, 3, 6, 12, 24, 9, 18, 36, 72, 27, 54, 108, 216, 5, 10, 20, 40, 15, 30, 60, 120, 45, 90, 180, 360, 135, 270, 540, 1080, 25, 50, 100, 200, 75, 150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternate construction: For n=1,2,... write all strings of length n using the first n symbols of an alphabet (a; aa,ab,ba,bb; aaa,aab,aac, aba,...), then code / interpret them as "positional" notation of exponents (a=0, b=1, ...) of primes (last digit = least prime), e.g.: bac => [1,0,2] => 5^1 3^0 2^2.

Obviously every natural numbers appears infinitely often (even after any other natural number) in this sequence. Thus any sequence of positive terms is a subsequence of this one.

A178484 is a more condensed version of this sequence.

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

The sequence begins: a(1)=2^0; a(2)=2^0 3^0, a(3)=2^1 3^0, a(4)=2^0 3^1, a(5)=2^1 3^1;

a(6,...)=2^0 3^0 5^0, 2^1 3^0 5^0, 2^2 3^0 5^0,

________ 2^0 3^1 5^0, 2^1 3^1 5^0, 2^2 3^1 5^0,

________ 2^0 3^2 5^0, 2^1 3^2 5^0, 2^2 3^2 5^0,

________ 2^0 3^0 5^1, 2^1 3^0 5^1, 2^2 3^0 5^1,

________ 2^0 3^1 5^1, 2^1 3^1 5^1, 2^2 3^1 5^1,

________ 2^0 3^2 5^1, 2^1 3^2 5^1, 2^2 3^2 5^1,

________ 2^0 3^0 5^2, 2^1 3^0 5^2, 2^2 3^0 5^2,

________ 2^0 3^1 5^2, 2^1 3^1 5^2, 2^2 3^1 5^2,

________ 2^0 3^2 5^2, 2^1 3^2 5^2, 2^2 3^2 5^2,...

PROG

(PARI) for( L=1, 4, forvec( v=vector(L, i, [0, L-1]), print1( prod( j=1, L, prime(j)^v[L-j+1] )", ")))

CROSSREFS

Cf. A178480, A178484.

Sequence in context: A107409 A268603 A226871 * A133031 A275732 A200594

Adjacent sequences:  A178480 A178481 A178482 * A178484 A178485 A178486

KEYWORD

nonn

AUTHOR

M. F. Hasler, May 31 2010

STATUS

approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)