A137625 - OEIS

%I #13 Jan 18 2025 15:36:16

%S 2,29,173,709,1741,8297,8297,19213,175229,175229,33952609,4377722623,

%T 4377722623,1242030992173,1242030992173

%N The initial prime in the first set of n consecutive primes for which p+4 is semiprime.

%C Suggested by Carlos Rivera's Puzzle 429 which asks for runs where p+2 is biprime.

%e a(2)=29 because this is the first prime in a run of 2 consecutive primes -- 29 and 31 -- where p+4 is semiprime, i.e., 29+4 and 31+4 are both semiprimes.

%o (UBASIC) 10 'p+4 is biprime 20 N=1 30 A=3:S=sqrt(N) 40 B=N\A: if B*A=N then N=N+2:goto 30 50 A=A+2: if A<=S then 40 60 C=C+1:O=N+4:D=prmdiv(O):E=O\D 70 if E<>prmdiv(E) or E=1 then C=0:goto 90 80 print C;N;D;E;O: if C>=10 then stop 90 N=N+2:goto 30

%Y Cf. A001358, A137626, A137627, A137628.

%K more,nonn

%O 1,1

%A _Enoch Haga_, Jan 30 2008

%E a(1) corrected and a(11)-a(15) from _Giovanni Resta_, Jun 22 2018

%E Example clarified by _Harvey P. Dale_, Jan 18 2025