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

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (1..3263 from K. D. Bajpai)

Example

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.

Mathematica

Select[Total /@ Partition[Select[Range[2000], Plus @@ Last /@ FactorInteger[#] == 2 && OddQ[#] &], 3, 1], PrimeQ]

Prog

(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++)<lim, if(bigomega(L)==2, u=concat(u, L); if(t>lim, break); if(isprime(t), listput(v, t)))); Vec(v) \\ Charles R Greathouse IV, Feb 03 2017

Crossrefs

Cf. A000040, A001358, A034961, A034962, A281824.

Sequence in context: A328160 A118162 A217076 * A139931 A325076 A353598

Adjacent sequences: A281957 A281958 A281959 * A281961 A281962 A281963

Keyword

nonn

Author

K. D. Bajpai, Feb 03 2017

Status

approved