A109805 a(n) = prime(n+2)*prime(n+1) - prime(n)*prime(n+1).

9, 20, 42, 66, 78, 102, 114, 230, 232, 248, 370, 246, 258, 470, 636, 472, 488, 670, 426, 584, 790, 830, 1246, 1164, 606, 618, 642, 654, 2034, 2286, 1310, 1096, 1668, 1788, 1208, 1884, 1630, 1670, 2076, 1432, 2172, 2292, 1158, 1182, 2786, 5064, 3568, 1362

Offset: 1

Author

Giovanni Teofilatto, Aug 16 2005

Keywords

• easy
• nonn

Comments

9 is the only semiprime of the form prime(n+2)*prime(n+1) - prime(n)*prime(n+1).

First differences of A006094. [Reinhard Zumkeller, Mar 13 2011]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006094.

The largest prime factor of a(n) gives the sequence A065091.

Programs

Mathematica

Table[Prime[n + 1]*(Prime[n + 2] - Prime[n]), {n, 48}] (* Ray Chandler, Aug 17 2005 *)
#[[2]](#[[3]]-#[[1]])&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Apr 01 2018 *)

Python

from sympy import prime, primerange
def aupton(nn):
    alst, prevp, prev_prod = [], 2, 6
    for p in primerange(3, prime(nn+2)+1):
        cur_prod = prevp * p
        alst.append(cur_prod - prev_prod)
        prevp = p
        prev_prod = cur_prod
    return alst[1:]
print(aupton(48)) # Michael S. Branicky, Sep 20 2021

Extensions

Edited and extended by Ray Chandler, Aug 17 2005