A354965 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.

4, 6, 9, 14, 10, 22, 39, 15, 35, 26, 46, 34, 49, 58, 25, 51, 21, 62, 69, 33, 38, 65, 77, 55, 57, 85, 94, 87, 95, 82, 91, 93, 111, 86, 121, 119, 143, 106, 129, 115, 123, 118, 122, 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

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Mathematica

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

Prog

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

Crossrefs

Cf. A001358 (semiprimes), A338309.

Sequence in context: A048625 A120134 A241451 * A288379 A112381 A182150

Adjacent sequences: A354962 A354963 A354964 * A354966 A354967 A354968

Keyword

nonn

Author

Zak Seidov, Jun 13 2022

Status

approved