A375647 Products of prime 8-tuples (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26) where p = A022012(n).

435656388001, 7667061486004435747476001, 26887071293271756518203932603297162186001, 1967190066500349361284627627321478140655499961186001, 34207121652717644163491129612663352350226660003697376196001, 131790860746164880099394335252801389818740796081899944471402001

Offset: 1

Author

Michael De Vlieger, Aug 24 2024

Keywords

• nonn

Comments

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

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).

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A022012, A128470, A375646, A375648.

Programs

Mathematica

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