cp's OEIS Frontend

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.

%I A280061 #21 Apr 07 2025 14:09:51
%S A280061 0,2,2,43,47,61,83,109,467,1453,2003,4909,18131,24877,32467,225581,
%T A280061 603859,944429,1267411,1485101,2447059,9349421,25253587,53389613,
%U A280061 88168147,100575533,151082707,989767981,3596703443,6738061613,6851483347
%N 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.
%C A280061 6851483347+21334239533=28185722880=2^28*3^1*5^1*7^1 (31-almost prime).
%C A280061 hence a(31) <= 21334239533.
%e A280061 a(0)+a(1)=0+2=2 (prime = 1-almost prime)
%e A280061 a(1)+a(2)=2+2=4 (semiprime prime = 2-almost prime)
%e A280061 a(2)+a(3)=2+43=45=2*2*5 (3-almost prime)
%e A280061 a(29)+a(30)=6738061613+6851483347=13589544960=2^25*3^4*5^1 (30-almost prime).
%t A280061 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 *)
%Y A280061 Cf. A001358, A116656.
%K A280061 nonn
%O A280061 0,2
%A A280061 _Zak Seidov_, Jan 30 2017