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

Author

Juri-Stepan Gerasimov, Aug 08 2008

Keywords

• nonn

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.

Examples

			  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)
		

Extensions

Edited by Jon E. Schoenfield, Feb 20 2021