A254325 Sequence of semiprimes with all cumulating sums being semiprime.

4, 6, 15, 26, 55, 111, 237, 469, 926, 1858, 3711, 7419, 14849, 29693, 59435, 118821, 237722, 475378, 950738, 1901474, 3802967, 7605921, 15211942, 30423869, 60847667, 121695326, 243390743, 486781401, 973562795, 1947125641, 3894251303, 7788502531, 15577005118

Offset: 1

Author

Zak Seidov, Feb 05 2015

Keywords

• nonn

Comments

a(1)=4, then a(n) is the least semiprime > a(n-1) such that a(1)+...+a(n) is semiprime.

Examples

			4+6=10=2*5, 10+15=25=5*5, 25+26=51=3*17.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..89

Crossrefs

Cf. A001358 (semiprimes), A065516.

Programs

Mathematica

s={4};a=4;Do[m=a+1;While[2!=PrimeOmega[m]||2!=PrimeOmega[m+a],m++]; AppendTo[s,m];a=m+a,{50}];s

PARI

{s=[4];a=4;
for(k=1,50,m=a+1while(2<>bigomega(m)||2<>bigomega(m+a),m++);
s=concat(s, m);a=m+a);s}