A380530 Positions of records in A380528.

1, 4, 10, 42, 366, 3246, 37266, 631266, 11563926, 271591926

Offset: 1

Author

Antti Karttunen, Feb 09 2025

Keywords

• nonn
• hard
• more

Comments

Questions: Are all terms squarefree after 4, and do all terms end (in base ten) with digit 6 from the fifth term onward? Is the sequence infinite? Are there any terms with more than four prime factors? See also the conjecture given in A380475, and A380476.

For n = 1..10, A380528(a(n)) = A008578(n). If a(11) exists, it is > 2^30.

Note that for squarefree n with exactly 5 prime factors (A046387), it might be possible that primes obtained as A380528(A046387(.)) has no upper limit. First k in A046387 such that A380528(k) is a prime 2 .. 17 are: 15015, 2730, 2310, 83886, 1551066, 71559186, 1245223986. See also the last two examples in A380470 for two similar cases with exactly 6 prime factors. - Antti Karttunen, May 08 2025

Links

• Index entries for sequences related to primorial base.

Crossrefs

Cf. A008578 (conjectured to give the record values), A046387, A380528, A380459, A380468, A380470, A380475, A380476.