A375264 -id:A375264 - cp's OEIS frontend

A376261 Products m of k = 5 consecutive primes p_1..p_k, where only p_1 < m^(1/k).

362469273063260281, 390268963330916339, 2501104163586622303, 9136139450993677127, 14786802713701223291, 16175430816211360949, 42275879149134880507, 58976503686022007233, 75786488186892877007, 124796858811854774081, 226284602311169194703, 252607170708747107509

Offset: 1

Michael De Vlieger, Sep 17 2024

nonn

In other words, products m of k = 5 consecutive primes p_1..p_k, where floor(log_p_1 m) >= k but floor(log_p_j m) = k-1, j > 1.
a(n) = m is such that floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.
Contains neither A375263 nor A375264, since for m in either sequence, both p_1 and p_2 are smaller than m^(1/k).

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

Cf. A375263, A375264, A376136.

k = 5; s = {1}~Join~Prime[Range[k - 1]]; Reap[Do[s = Append[Rest[s], Prime[i + k - 1]]; r = Surd[Times @@ s, k]; If[Count[s, _?(# < r &)] == 1, Sow[Times @@ s] ], {i, 120}] ][[-1, 1]]

A375263 Products of prime 5-tuples (p, p+2, p+6, p+8, p+12) where p = A022006(n).

Original entry on oeis.org

85085, 1062347, 13710311357, 7260418981910177, 1070581737243007155797, 2766839311485334046837, 4100268039496291731347, 5485857138434357935487, 160955606471252225494877, 518874528458711923617827, 62276368576118330117536697, 124939289421198925662649757, 129296510584439756429395217

Offset: 1

Michael De Vlieger, Aug 16 2024

nonn

Subsequence of A046387.

Aside from a(1) = 85085 = 5 (mod 30), all terms are congruent to 17 (mod 30), since a(k), k > 2 is a product m of the following residues (mod 30): {11, 13, 17, 19, 23}, and m mod 30 is congruent to 17.

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

Cf. A022006, A046387, A375264.

Map[Times @@ NextPrime[#, Range[0, 4]] &, Select[Prime@ Range[2^16], AllTrue[{# + 2, # + 6, # + 8, # + 12}, PrimeQ] &]]

cp's OEIS Frontend

A376261 Products m of k = 5 consecutive primes p_1..p_k, where only p_1 < m^(1/k).

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