A116656 Slowest growing sequence of semiprimes having the semiprime-pairwise-sum property: for any i

4, 6, 51, 115, 511, 5263, 116623, 204091, 823363, 1144363, 78325123, 883337023, 6860264683, 19613836423, 167589841663

Offset: 1

Author

Zak Seidov, Feb 21 2006

Keywords

• nonn
• hard
• more

Examples

			Triangle of resulting semiprimes begins:
      10
      55,     57
     119,    121,    166
     515,    517,    562,    626
    5267,   5269,   5314,   5378,   5774
  116627, 116629, 116674, 116738, 117134, 121886
		

Crossrefs

Cf. A001358, A164979, A181620.

Programs

Mathematica

spQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; L = {0, 4}; Do[n = L[[-1]] + 1; While[! AllTrue[n + L, spQ], n++]; AppendTo[L, n], {9}]; Rest@ L (* Giovanni Resta, Jun 13 2018 *)

PARI

lista(nn) = my(m, r, s, t, u, v=vector(nn=max(2, nn))); print1(v[1]=4, ", ", v[2]=6); for(n=3, nn, m=4; r=List([3]); forprime(p=2, oo, if(m*p>v[n-1], break); u=List([]); forprime(q=2, p-1, s=Set(v%(t=p*q)); for(i=1, #s, listput(u, Mod(t-s[i], t)))); s=List([]); for(i=1, #r, forstep(k=r[i], m*p, m, t=1; for(j=1, #u, if(k==u[j], t=0; break)); if(t, listput(s, k)))); r=s; m*=p); listsort(r); forstep(i=0, oo, m, for(j=1, #r, t=i+r[j]; if(t>v[n-1]&&bigomega(t)==2&&bigomega(t+4)==2&&bigomega(t+6)==2, for(k=3, n-1, if(!isprime((t+v[k])\2), t=0; break)); if(t, print1(", ", v[n]=t); break(2)))))); \\ Jinyuan Wang, May 29 2025

Extensions

a(8)-a(10) from R. J. Mathar, Jan 23 2008

a(11)-a(12) from Donovan Johnson, Nov 11 2008

a(13) from Donovan Johnson, Jul 22 2011

a(14) from Giovanni Resta, Jun 13 2018

a(15) from Giovanni Resta, Jun 14 2018