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
Ivan Neretin, Table of n, a(n) for n = 1..10000
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,...
MATHEMATICA
{1}~Join~Flatten@Table[Times @@ (Prime@Range@n^Reverse@PadLeft[ IntegerDigits[#, n], n]) & /@ (Range[n^n] - 1), {n, 2, 4}] (* Ivan Neretin, May 02 2019 *)
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 31 2010
STATUS
approved