A280061 a(0)=0; thereafter a(n) is the smallest prime not less than a(n-1) such that a(n - 1) + a (n) is a product of n primes.

0, 2, 2, 43, 47, 61, 83, 109, 467, 1453, 2003, 4909, 18131, 24877, 32467, 225581, 603859, 944429, 1267411, 1485101, 2447059, 9349421, 25253587, 53389613, 88168147, 100575533, 151082707, 989767981, 3596703443, 6738061613, 6851483347

Offset

0,2

Comments

6851483347+21334239533=28185722880=2^28*3^1*5^1*7^1(31-almost prime).

hence a(31) <= 21334239533.

Links

Table of n, a(n) for n=0..30.

Example

a(0)+a(1)=0+2=2 (prime = 1-almost prime)
a(1)+a(2)=2+2=4 (semiprime prime = 2-almost prime)
a(2)+a(3)=2+43=45=2*2*5 (3-almost prime)
a(29)+a(30)=6738061613+6851483347=13589544960=2^25*3^4*5^1 (30-almost prime).

Mathematica

f[n_] := f[n] =  Block[{p = f[n - 1], q = NextPrime[ f[n - 1] - 1]}, While[ PrimeOmega[p + q] != n, q = NextPrime@ q]; q]; f[0] = 0; Array[f, 22] (* Robert G. Wilson v, Jan 30 2017 *)

Crossrefs

Cf. A001358, A116656.

Sequence in context: A264516 A271845 A348226 * A349602 A156467 A303538

Adjacent sequences: A280058 A280059 A280060 * A280062 A280063 A280064

Keyword

nonn

Author

Zak Seidov, Jan 30 2017

Status

approved