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

1,2

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A005228, A030124.

The complement is A286290, excluding the initial 1.

Sequence in context: A303234 A175233 A346130 * A286291 A286926 A145198

Adjacent sequences: A121226 A121227 A121228 * A121230 A121231 A121232

Keyword

easy,nonn

Author

Giovanni Teofilatto, Aug 21 2006

Status

approved