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A080377
Each a(n) is a difference of suitable consecutive primes, a(n)=Prime[1+A080376(n)]-Prime[A080376(n)]. a(n+1) is the smallest prime-difference [from A001223] which has prime-factor not present in previous terms or was present but at lower power.
0
2, 4, 6, 8, 14, 10, 18, 22, 34, 16, 26, 32, 38, 50, 62, 54, 58, 46, 64, 86, 82, 74, 98, 106, 94, 118, 122, 128, 146, 134, 142, 162, 178, 158
OFFSET
1,1
EXAMPLE
18 is the 7th term:in first-6th ones {2,4,6,8,14,10} 3 does not occur with power 2 unlike in 18; 22 is the 8th term: in first-7th terms 11 is not a prime factor unlike 22. several even numbers do not arise in this sequence, e.g.:12,20,36,48, etc..
MATHEMATICA
s=1; Do[s1=s; s=LCM[s, d=Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[d]], {n, 1, 10000000}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 27 2003
STATUS
approved