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Products of prime 8-tuples (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26) where p = A022012(n).
3

%I #5 Sep 11 2024 00:41:28

%S 435656388001,7667061486004435747476001,

%T 26887071293271756518203932603297162186001,

%U 1967190066500349361284627627321478140655499961186001,34207121652717644163491129612663352350226660003697376196001,131790860746164880099394335252801389818740796081899944471402001

%N Products of prime 8-tuples (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26) where p = A022012(n).

%C Primes p in A022012 belong to either 17 or 167 (mod 210).

%C Therefore a(n) is either congruent to the product of residues {17, 19, 23, 29, 31, 37, 41, 43} (mod 210), or {167, 169, 173, 179, 181, 187, 191, 193} (mod 210), so a(n) is congruent to 121 (mod 210).

%C Gaps between prime factors have a symmetric arrangement {2, 4, 6, 2, 6, 4, 2}.

%H Michael De Vlieger, <a href="/A375647/b375647.txt">Table of n, a(n) for n = 1..10000</a>

%t Map[Times @@ NextPrime[#, Range[0, 7]] &, Import["https://oeis.org/A022012/b022012.txt", "Data"][[;; 12, -1]]]

%Y Cf. A022012, A128470, A375646, A375648.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Aug 24 2024