

A321503


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


6



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
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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



