A121229 Beginning with a(1) = 1 and a(2) = 2, a(n) is not equal to the product of two consecutive (distinct) earlier terms.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset: 1

Author

Giovanni Teofilatto, Aug 21 2006

Keywords

• easy
• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005228, A030124.

The complement is A286290, excluding the initial 1.

Programs

Maple

A121229 := proc(n)
    option remember;
    local a,ispr,i;
    if n <=2 then
        n;
    else
        for a from procname(n-1)+1 do
            ispr := false ;
            for i from 1 to n-2 do
                if procname(i)*procname(i+1) = a then
                    ispr := true ;
                    break;
                end if;
            end do:
            if not ispr then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, May 25 2017

Mathematica

a[n_] := a[n] = Module[{k, ispr, i}, If[n <= 2, n, For[k = a[n - 1] + 1, True, k++, ispr = False; For[i = 1, i <= n - 2, i++, If[a[i]*a[i + 1] == k, ispr = True; Break[]]]; If[!ispr, Return[k]]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 23 2022, after R. J. Mathar *)

Python

from itertools import islice
def agen(): # generator of terms
    disallowed, prevk, k = {1, 2}, 2, 3; yield from [1, 2]
    while True:
        while k in disallowed: k += 1
        yield k; disallowed.update([k, k*prevk]); prevk = k
print(list(islice(agen(), 72))) # Michael S. Branicky, Sep 23 2022