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A373790
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The term that immediately precedes prime(n) in A373390.
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4
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1, 2, 14, 6, 39, 11, 38, 17, 75, 62, 29, 117, 80, 88, 98, 165, 122, 59, 136, 207, 217, 231, 253, 265, 196, 297, 305, 323, 321, 329, 375, 385, 407, 411, 445, 447, 316, 483, 495, 513, 531, 535, 555, 561, 573, 583, 621, 651, 669, 675, 687, 705, 711, 735, 753, 767, 785, 789, 801, 819, 825, 855, 889
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OFFSET
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1,2
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COMMENTS
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In order for A373390 to contain a prime term, say a(i) = p, then there must be at least one earlier term which is a multiple of p, say a(j) = k*p with k>1 and j<i.
Conjectures:
(C1): For each prime p > 3, there is exactly one multiple of p that appears before p itself. Call this multiple k*p. Note that we know (see the Comments in A373390) that every prime appears in A373390. We will call this multiple k*p the term that "introduces" p.
(C2): For every prime p > 3, the introducing term k*p is always either 2*p or 3*p, and for all except the eleven primes listed in A372078 it is 2*p.
(C3): For every prime p > 3, the introducing term k*p occurs exactly 2 terms before p itself, with the single exception of A373390(11) = 7 which is introduced in A373390 three terms earlier, by A373390(8) = 14.
(C4): The primes appear in A373390 in their natural order. That is, if p<q are primes, then p appears before q. Furthermore, if k*p is the first multiple of p that appears and m*q is the first multiple of q that appears, then k*p appears before m*q.
Based on the limited number of known prime terms in the present sequence, i.e., 2, 11, 17, 29 and 59, it seems that for every a(n) that is prime, a(n) = A000040(n-1). - Ivan N. Ianakiev, Jun 22 2024
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LINKS
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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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