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 A243904 Semiprimes of the form p^2 + pq + q^2, where p, q are consecutive primes. 1
 49, 247, 679, 973, 2701, 5293, 7509, 10801, 12297, 15553, 17337, 25963, 29407, 33079, 34993, 36967, 43249, 53877, 67501, 71157, 76809, 97201, 117613, 155953, 181573, 225237, 270049, 292033, 297679, 314977, 350917, 380217, 477607, 492091, 514213, 632047, 648679 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A001358 and A003136. LINKS K. D. Bajpai, Table of n, a(n) for n = 1..10000 EXAMPLE 247 is in the sequence because 7^2 + 7*11 + 11^2 = 247 = 13*19, which is semiprime. 679 is in the sequence because 13^2 + 13*17 + 17^2 = 679 = 7*97, which is semiprime. MAPLE with(numtheory): A243904:= proc() local k, p, q; p:=ithprime(n); q:=ithprime(n+1); k:=p^2 + p*q + q^2; if bigomega(k)=2 then RETURN (k); fi; end: seq(A243904 (), n=1..200); MATHEMATICA Select[Table[Prime[n]^2 + Prime[n] Prime[n + 1] + Prime[n + 1]^2, {n, 100}], PrimeOmega[#] == 2 &] PROG (PARI) issemi(n)=bigomega(n)==2 list(lim)=my(v=List(), p=3, t); forprime(q=5, , t=p^2+p*q+q^2; if(t>lim, break); if(issemi(t), listput(v, t)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 05 2017 CROSSREFS Cf. A001358, A007945, A003136, A243761. Sequence in context: A373680 A322675 A260198 * A017246 A020274 A158248 Adjacent sequences: A243901 A243902 A243903 * A243905 A243906 A243907 KEYWORD nonn AUTHOR K. D. Bajpai, Jun 14 2014 STATUS approved

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Last modified July 23 19:43 EDT 2024. Contains 374553 sequences. (Running on oeis4.)