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Products of prime triples (p, p+4, p+6) where p = A022005(n).
1

%I #17 Jun 30 2024 16:29:44

%S 1001,4199,65231,347261,1009091,1201289,7566179,11592209,22027871,

%T 29884301,97543451,234118799,564234809,627947039,682238471,1296207281,

%U 2198678291,2901757409,3050714441,3283574069,4626836849,4881262679,5700149369,6542683061,6605851859,7956061979

%N Products of prime triples (p, p+4, p+6) where p = A022005(n).

%C Subsequence of A120944, subsequence of A007304.

%C Terms are congruent to 5 (mod 6), since A022005(n) is congruent to 1 mod 6, and 5+4 and 5+6 are congruent to 5 and 1 (mod 6), respectively. The product 1*5*1 is congruent to 5 (mod 6).

%e a(1) = 1001 = 7 * 11 * 13.

%e a(2) = 4199 = 13 * 17 * 19.

%e a(3) = 65231 = 37 * 41 * 43, etc.

%t Map[Times @@ NextPrime[#, {0, 1, 2}] &, Select[Prime@ Range[320], AllTrue[{# + 4, # + 6}, PrimeQ] &]]

%Y Cf. A007304, A016969, A022005, A120944.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Jun 29 2024