A272306 Lesser of two consecutive semiprimes whose sum is also semiprime.

4, 6, 25, 34, 38, 39, 46, 51, 57, 65, 69, 77, 87, 93, 95, 106, 111, 118, 129, 133, 145, 146, 161, 166, 169, 177, 178, 187, 194, 201, 205, 206, 209, 213, 218, 221, 249, 262, 278, 291, 298, 305, 309, 314, 323, 334, 335, 341, 355, 361, 377, 381, 394, 395, 407, 422, 446, 447, 473

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

51 is in the sequence because 51 = 3*17, the next semiprime is 55 = 5*11, and 51+55 = 106 = 2*53, is also semiprime.

Mathematica

s[n_] := PrimeOmega@n == 2; L = Select[Range@480, s]; Pick[ Most@L, s /@ (Plus @@@ Partition[L, 2, 1])] (* Giovanni Resta, Apr 25 2016 *)
Select[Partition[Select[Range[500], PrimeOmega[#]==2&], 2, 1], PrimeOmega[ Total[ #]] == 2&][[All, 1]] (* Harvey P. Dale, Jul 10 2018 *)

Prog

(PARI) proxsem(n)=my(p=n, s, r); while(s==0, p++; if(bigomega(p)==2, s=1; r=p)); p
{for(i=1, 500, if(bigomega(i)==2, a=proxsem(i); if(bigomega(a+i)==2, print1(i, ", "))))}
(PARI) issemi(n)=bigomega(n)==2
list(lim)=my(v=List(), u=v); lim\=1; while(bigomega(lim++)!=2, ); forprime(p=2, lim\2, forprime(q=2, lim\p, listput(v, p*q))); v=Set(v); for(i=1, #v-1, if(issemi(v[i+1]+v[i]), listput(u, v[i]))); Set(u) \\ Charles R Greathouse IV, Apr 29 2016

Crossrefs

Cf. A001358, A272307, A272308, A272309.

Sequence in context: A009459 A239625 A123055 * A294996 A176858 A182333

Adjacent sequences: A272303 A272304 A272305 * A272307 A272308 A272309

Keyword

nonn

Author

Antonio Roldán, Apr 25 2016

Status

approved