A354965 - OEIS

%I #12 Aug 05 2022 07:43:46

%S 4,6,9,14,10,22,39,15,35,26,46,34,49,58,25,51,21,62,69,33,38,65,77,55,

%T 57,85,94,87,95,82,91,93,111,86,121,119,143,106,129,115,123,118,122,

%U 74,133,142,166,145,158,202,169,177,141,146,159,183,134,203,161,187,155,178,201,215,185,206,209,194

%N a(1) = 4, a(2) = 6; a(3) = 9; thereafter a(n) is the smallest new semiprime such that the sum of four successive terms is semiprime.

%t s = {4, 6, 9}; Do[a = s[[-1]] + s[[-2]] + s[[-3]]; n = 10; While[MemberQ[s, n] || 2 != PrimeOmega[n] || 2 != PrimeOmega[a + n], n++]; AppendTo[s, n], {120}]; s

%o (PARI) issp(k) = bigomega(k)==2; \\ A001358

%o lista(nn) = my(va = vector(nn)); va[1]=4; va[2]=6; va[3]=9; my(vs = vecsort(va)); my(s=sum(k=1, 3, va[k])); for (n=4, nn, my(k=1); while (!(issp(k) && issp(k+s) && !vecsearch(vs, k)), k++); va[n]=k; vs = vecsort(va); s += k - va[n-3];); va; \\ _Michel Marcus_, Aug 04 2022

%Y Cf. A001358 (semiprimes), A338309.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 13 2022