A230518 Smallest prime p = a(n) such that the sum of p and the next prime has n distinct prime factors.

2, 5, 13, 103, 1783, 15013, 285283, 9699667, 140645501, 4127218087, 100280245063, 5625398263453, 202666375276361, 11602324073775431, 438272504610946003, 21828587281891445047, 1156915125940246587913, 66595945348137856405747, 4632891063696575353839163

Offset: 1

Author

Jean-François Alcover, Oct 22 2013

Keywords

• nonn

Examples

			30 = 13+17 is the earliest case with 3 prime divisors, so a(3) = 13.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A001043, A071215, A071216, A098037, A105418.

Programs

Mathematica

Clear[a]; a[_] = 0; Do[p = Prime[k]; q = Prime[k+1]; n = PrimeNu[p+q]; If[a[n] == 0, a[n] = p; Print["a(", n, ") = p = ", p, ", q = ", q]], {k, 1, 10^9}]; Table[a[n], {n, 1, 10}]

PARI

a(n) = {p = 2; while (omega(p+nextprime(p+1)) != n, p = nextprime(p+1)); p;} \\ Michel Marcus, Oct 22 2013

PARI

step(Fvec)=my([n,f]=Fvec,v=List(),t);for(i=1,#f~,t=f;t[i,2]++;listput(v,[n*f[i,1],t]);t=f;t[i,1]=nextprime(t[i,1]+1);if(i==#f~||t[i,1]1,1,prime(i))),v=[[factorback(f),f]],t); if(!bad(v[1][1]),return(precprime(v[1][1]/2))); v=vecsort(step(v[1]),1); while(bad(v[1][1]), v=vecsort(concat(step(v[1]),v[2..#v]),1,8)); precprime(v[1][1]/2); \\ Charles R Greathouse IV, Oct 22 2013

Formula

a(n) > (1/2 + o(1)) n^n. - Charles R Greathouse IV, Oct 22 2013

Extensions

a(11)-a(19) from Charles R Greathouse IV, Oct 22 2013