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A109805
a(n) = prime(n+2)*prime(n+1) - prime(n)*prime(n+1).
4
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
1,1
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
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 *)
PROG
(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
CROSSREFS
Cf. A006094.
The largest prime factor of a(n) gives the sequence A065091.
Sequence in context: A143704 A128153 A249044 * A345727 A332372 A377002
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Aug 16 2005
EXTENSIONS
Edited and extended by Ray Chandler, Aug 17 2005
STATUS
approved