A375646 -id:A375646 - cp's OEIS frontend

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

Michael De Vlieger, Aug 24 2024

nonn

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}.

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

Cf. A022012, A128470, A375646, A375648.

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

A375648 Products of prime 8-tuples (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26) where p = A022013(n).

Original entry on oeis.org

3868985835982814590518552822749329543261, 43207320984601757696213691690377119115644261, 287530494211069388143263747303929618940138523261, 2991325021830996455943969680355510324042937309261, 3433715221252595293789329211184553889095776281330363261, 523198428668721638888114210837839571392856841008842698982189261

Offset: 1

Michael De Vlieger, Aug 24 2024

nonn

Primes p in A022013 belong to 173 (mod 210). Thus a(n) is congruent to the product of residues {173, 179, 181, 187, 191, 193, 197, 199} (mod 210), i.e., 1 (mod 210).

Gaps between primes are {6, 2, 6, 4, 2, 4, 2}.

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

Cf. A022012, A128470, A375646, A375647.

Map[Times @@ NextPrime[#, Range[0, 7]] &, Import["https://oeis.org/A022013/b022013.txt", "Data"][[;; 12, -1]]]

cp's OEIS Frontend

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).

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