A281960 Primes that are the sum of three consecutive odd semiprimes.
61, 79, 107, 139, 163, 191, 211, 263, 271, 373, 443, 617, 719, 733, 761, 971, 991, 1097, 1129, 1231, 1259, 1373, 1439, 1531, 1543, 1597, 1663, 1697, 1733, 1753, 1777, 1831, 2053, 2081, 2099, 2137, 2161, 2213, 2383, 2423, 2543, 2677, 2687, 2719, 2777, 2843, 2917
Offset: 1
Keywords
Examples
a(1) = 61 is a prime and 61 = 15 + 21 + 25; the sum of three consecutive odd semiprimes. a(2) = 79 is a prime and 79 = 21 + 25 + 33; the sum of three consecutive odd semiprimes.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (1..3263 from K. D. Bajpai)
Programs
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Mathematica
Select[Total /@ Partition[Select[Range[2000], Plus @@ Last /@ FactorInteger[#] == 2 && OddQ[#] &], 3, 1], PrimeQ]
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PARI
list(lim)=my(v=List(),u=v,t,L=lim+10); forprime(p=3,L\3, forprime(q=3,min(p,L\p), listput(u,p*q))); u=Set(u); for(i=3,#u, if(isprime(t=u[i-2]+u[i-1]+u[i]), listput(v,t))); while((t=u[#u-1]+u[#u]+L++)