A141465 Prime transformed products of prime factors of the composites, the largest prime decremented by 2, the smallest by 1.

2, 3, 2, 5, 3, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481

Offset

1,1

Comments

In the prime factorization of k=A002808(i), i=1,2,3,..., one instance of the largest prime, pmax=A052369(i), is replaced by pmax-2 and one instance of the smallest prime, pmin=A056608(i), is replaced by pmin-1. If the product of this modified set of factors, k*(pmax-2)*(pmin-1)/(pmin*pmax), is prime, it is appended to the sequence.

Links

Table of n, a(n) for n=1..52.

Example

  composite k     transformed product
  -----------  -------------------------
   4 = 2*2     (2-1)*(2-2)   = 1*0   = 0  (nonprime)
   6 = 2*3     (2-1)*(3-2)   = 1*1   = 1  (nonprime)
   8 = 2*2*2   (2-1)*2*(2-2) = 1*2*0 = 0  (nonprime)
   9 = 3*3     (3-1)*(3-2)   = 2*1   = 2  = a(1)
  10 = 2*5     (2-1)*(5-2)   = 1*3   = 3  = a(2)
  12 = 2*2*3   (2-1)*2*(3-2) = 1*2*1 = 2  = a(3)
  14 = 2*7     (2-1)*(7-2)   = 1*5   = 5  = a(4)

Crossrefs

Sequence in context: A094020 A165609 A358462 * A263216 A141663 A011153

Adjacent sequences: A141462 A141463 A141464 * A141466 A141467 A141468

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 08 2008

Extensions

Edited by Jon E. Schoenfield, Feb 20 2021

Status

approved