A321503 Numbers m such that m and m+1 both have at least 3 distinct prime factors.

230, 285, 429, 434, 455, 494, 560, 594, 609, 615, 644, 645, 650, 665, 714, 740, 741, 759, 804, 805, 819, 825, 854, 860, 884, 902, 935, 945, 969, 986, 987, 1001, 1014, 1022, 1034, 1035, 1044, 1064, 1065, 1070, 1085, 1104, 1105, 1130, 1196, 1209, 1220, 1221, 1235, 1239, 1245, 1265

Offset

1,1

Comments

Disjoint union of A140077 (omega({m, m+1}} = {3}) and A321493 (not both have exactly 3 prime divisors). The latter contains terms with indices {15, 60, 82, 98, 99, 104, ...} of this sequence.

Numbers m and m+1 can never have a common prime factor (consider them mod p), therefore the terms are > sqrt(A002110(3+3)), A002110 = primorial.

Links

M. F. Hasler, Table of n, a(n) for n = 1..10000

Mathematica

aQ[n_]:=Module[{v={PrimeNu[n], PrimeNu[n+1]}}, Min[v]>2]; Select[Range[1300], aQ] (* Amiram Eldar, Nov 12 2018 *)

Prog

(PARI) select( is(n)=omega(n)>2&&omega(n+1)>2, [1..1300])

Crossrefs

Cf. A255346, A321504 .. A321506, A321489 (analog for k = 2, ..., 7 prime divisors).

Cf. A321493, A321494 .. A321497 (subsequences of the above: m or m+1 has more than k prime divisors).

Cf. A074851, A140077, A140078, A140079 (complementary subsequences: m and m+1 have exactly k = 2, 3, 4, 5 prime divisors).

Sequence in context: A177826 A122269 A171666 * A140077 A215217 A291617

Adjacent sequences: A321500 A321501 A321502 * A321504 A321505 A321506

Keyword

nonn

Author

M. F. Hasler, Nov 13 2018

Status

approved