A373790 The term that immediately precedes prime(n) in A373390.

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

Offset: 1

Author

N. J. A. Sloane, Jun 21 2024

Keywords

• nonn

Comments

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

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

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

Examples

			A373390(24) = 11 = prime(5), so a(5) = A373390(23) = 39.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..40005 (First 6267 terms from N. J. A. Sloane)

Crossrefs

Cf. A373390, A372072, A372073, A372078-A372081, A373786-A373791.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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