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A285689 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of four primes.

%I A285689 #11 Nov 28 2019 22:51:52
%S A285689 2,83,107,131,167,191,227,251,307,331,347,383,419,443,467,491,547,563,
%T A285689 587,641,677,701,757,773,797,821,857,881,937,953,977,1013,1049,1103,
%U A285689 1163,1187,1223,1259,1283,1307,1361,1451,1487,1511,1567,1583,1607,1663,1699,1723,1747,1783,1823
%N A285689 a(1) = 2; a(n + 1) = smallest prime > a(n) such that a(n + 1) - a(n) is the product of four primes.
%C A285689 First differences: 81, 24, 24, 36, 24, 36, 24, 56, 24, 16, 36, 36, 24, 24, 24, 56, 16, 24, 54, 36, 24,...
%H A285689 Robert Israel, <a href="/A285689/b285689.txt">Table of n, a(n) for n = 1..10000</a>
%p A285689 A[1]:= 2: p:= 2: n:= 1:
%p A285689 while n < 60 do
%p A285689     p:= nextprime(p);
%p A285689     if numtheory:-bigomega(p-A[n]) = 4 then n:= n+1; A[n]:= p; fi
%p A285689 od:
%p A285689 seq(A[i],i=1..60); # _Robert Israel_, Nov 28 2019
%t A285689 NestList[Module[{p = NextPrime@ #}, While[PrimeOmega[p - #] != 4, p = NextPrime@ p]; p] &, 2, 52] (* _Michael De Vlieger_, Apr 25 2017 *)
%Y A285689 Cf. A255609, A285688.
%K A285689 nonn
%O A285689 1,1
%A A285689 _Zak Seidov_, Apr 24 2017