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A373656
a(n) is the n-th prime after the n-th semiprime.
1
5, 11, 17, 19, 31, 37, 47, 53, 61, 67, 79, 83, 89, 101, 103, 113, 131, 137, 149, 151, 157, 173, 179, 191, 199, 211, 227, 233, 239, 241, 257, 263, 269, 271, 293, 313, 331, 337, 347, 349, 353, 359, 373, 383, 389, 409, 419, 421, 431, 433, 449, 461, 463, 467, 487, 499, 509, 521, 547, 557, 563, 577
OFFSET
1,1
LINKS
FORMULA
a(n) = A000040(n + A000720(A001358(n))).
EXAMPLE
a(5) = 31 because the 5th semiprime is 14 and the first 5 primes after 14 are 17, 19, 23, 29, 31.
MAPLE
N:= 1000: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]): nP:= nops(P):
S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]):
f:= proc(n) local j;
j:= ListTools:-BinaryPlace(P, S[n]);
if j + n <= nP then P[j+n] else fail fi
end proc:
R:= NULL:
for i from 1 do
v:= f(i);
if v = fail then break fi;
R:= R, v
od:
R;
MATHEMATICA
sp=Select[Range[200], PrimeOmega[#]==2&]; Table[NextPrime[sp[[n]], n], {n, 62}] (* James C. McMahon, Jul 07 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov and Robert Israel, Jun 14 2024
STATUS
approved