A243904 Semiprimes of the form p^2 + pq + q^2, where p, q are consecutive primes.

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

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: A211761 A322675 A260198 * A017246 A020274 A158248

Adjacent sequences: A243901 A243902 A243903 * A243905 A243906 A243907

Keyword

nonn

Author

K. D. Bajpai, Jun 14 2014

Status

approved