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A353408
a(n) is the least new prime number such that a(n) + a(n-1) is a semiprime.
2
2, 7, 3, 11, 23, 59, 47, 71, 107, 167, 131, 83, 179, 347, 191, 263, 239, 227, 251, 311, 383, 419, 359, 443, 479, 503, 431, 467, 491, 647, 587, 599, 683, 719, 563, 743, 659, 827, 887, 839, 983, 911, 863, 1019, 947, 1091, 971, 1151, 1031, 1163, 1223, 1103, 1259, 1187, 1367, 1451, 1283, 1319, 1427, 1307, 1439, 1523, 1499
OFFSET
1,1
COMMENTS
Starting with a(3) = 3, (a(n) + a(n-1))/2 is a prime.
For n >= 4, a(n) == 11 (mod 12). Conjecture: every prime == 11 (mod 12) occurs in the sequence. - Robert Israel, Mar 04 2023
LINKS
EXAMPLE
2+7=9=3*3, 7+3=10=2*5, 3+11=14=2*7 are all semiprimes.
MAPLE
R:= 2, 7: p:= 7: P:= select(isprime, [3, seq(i, i=11..2000, 12)]):
nP:= nops(P): count:= 2:
do
found:= false;
for k from 1 to nops(P) do
q:= P[k];
if isprime((p+q)/2) then
found:= true; count:= count+1; p:= q; R:= R, p; P:= subsop(k=NULL, P); nP:= nP-1; break
fi
od;
if not found then break fi;
od:
R; # Robert Israel, Mar 04 2023
MATHEMATICA
s = {2}; Do[p = 2; While[! FreeQ[s, p] || PrimeOmega[s[[-1]] + p] > 2, p = NextPrime[p]]; AppendTo[s, p], {200}]; s
CROSSREFS
Sequence in context: A304754 A091578 A332363 * A365966 A258249 A256448
KEYWORD
nonn
AUTHOR
Zak Seidov, May 07 2022
STATUS
approved