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A360549
a(n) is the least prime p not already in the sequence such that a(n-1) + p is a triprime; a(1) = 2.
1
2, 43, 7, 5, 3, 17, 11, 19, 23, 29, 13, 31, 37, 41, 61, 53, 71, 59, 79, 103, 67, 47, 83, 89, 97, 73, 101, 137, 107, 131, 113, 109, 127, 139, 151, 167, 149, 173, 181, 157, 197, 191, 163, 193, 211, 199, 227, 179, 223, 229, 241, 233, 349, 257, 251, 283, 307, 271, 263, 293, 281, 317, 239, 269, 313
OFFSET
1,1
COMMENTS
Conjecture: every prime eventually appears in the sequence.
LINKS
EXAMPLE
a(4) = 5 because 5 is a prime that has not yet occurred in the sequence, a(4) + 5 = 12 = 2^2^3 is a triprime; the only other prime (3) that has not yet occurred does not work because a(4) + 3 = 10 = 2*5 is not a triprime.
MAPLE
R:= 2: p:= 2: P:= select(isprime, [seq(i, i=3..10000, 2)]):
do
found:= false;
for k from 1 to nops(P) do
q:= P[k];
if numtheory:-bigomega(q+p) = 3 then
found:= true; p:= q; R:= R, p; P:= subsop(k=NULL, P); break
fi
od;
if not found then break fi;
od:
R;
CROSSREFS
Sequence in context: A052078 A069544 A256285 * A268467 A236695 A085460
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Mar 04 2023
STATUS
approved