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A397769
a(1) = 1; a(n+1) = a(n) * (2^a(n) + 1).
0
1, 3, 27, 3623878683
OFFSET
1,2
COMMENTS
a(5) contains 1090896194 digits and is too large to include.
This sequence arises in the card game Magic: The Gathering. You start with a card called Doubling Season, which doubles all token copies you create. When you make a token copy of all Doubling Seasons you control on the battlefield simultaneously, the total number of Doubling Seasons you have afterwards is the next term.
A034797 is the sequence you get if you make a copy of only one Doubling Season at each step instead of all of them.
LINKS
Wizards of the Coast, Doubling Season.
Wizards of the Coast, Rules of Magic: The Gathering.
EXAMPLE
a(2) = 1 + 1*2^1 = 3.
MATHEMATICA
NestList[#*(2^# + 1) &, 1, 3] (* Paolo Xausa, Aug 27 2026 *)
PROG
(Python)
def A(n):
a = 1
for _ in range(n):
a = a * (1 + 2**a)
return a
print([A(n) for n in range(4)])
CROSSREFS
Cf. A034797.
Sequence in context: A308384 A381168 A055777 * A014222 A162414 A071107
KEYWORD
nonn,new
AUTHOR
Joshua B. Weinstein, Aug 13 2026
STATUS
approved