OFFSET
0,2
EXAMPLE
After the 1st step the set becomes {1*1, 1+1} = {1, 2}. It has 2 distinct elements so a(1) = 2.
After the 2nd step the set becomes {1*1, 1+1, 1*2, 1+2, 2*2, 2+2} = {1, 2, 2, 3, 4, 4} = {1, 2, 3, 4}. It has 4 distinct elements so a(2) = 4.
MATHEMATICA
Length /@ NestList[DeleteDuplicates[Flatten[Table[With[{a = #[[k]], b = #[[;; k]]}, {a b, a + b}], {k, Length[#]}]]] &, {1}, 6]
PROG
(PARI) lista(nn) = {my(v = [1]); print1(#v, ", "); for (n=1, nn, v = setunion(setbinop((x, y)->(x+y), v), setbinop((x, y)->(x*y), v)); print1(#v, ", "); ); } \\ Michel Marcus, Apr 13 2022
(Python)
from math import prod
from itertools import combinations_with_replacement
from functools import lru_cache
@lru_cache(maxsize=None)
def A352969_set(n):
if n == 0:
return {1}
return set(sum(x) for x in combinations_with_replacement(A352969_set(n-1), 2)) | set(prod(x) for x in combinations_with_replacement(A352969_set(n-1), 2))
def A353969(n):
return len(A352969_set(n)) # Chai Wah Wu, Apr 15 2022
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Vladimir Reshetnikov, Apr 12 2022
EXTENSIONS
a(7) from Thomas Scheuerle, Apr 13 2022
a(7) corrected by Chai Wah Wu, Apr 15 2022
STATUS
approved