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A283267
Smallest b-a such that a < prime(n) < b, where a,b are semiprimes.
3
2, 3, 4, 4, 6, 6, 3, 7, 7, 3, 7, 7, 3, 4, 4, 4, 4, 5, 5, 5, 3, 4, 11, 11, 11, 5, 5, 4, 6, 4, 7, 7, 9, 9, 3, 5, 3, 8, 5, 5, 7, 7, 7, 7, 4, 5, 9, 9, 9, 10, 10, 4, 5, 3, 7, 7, 4, 9, 9, 4, 4, 5, 5, 5, 5, 4, 9, 9, 9, 3, 6, 6, 4, 4, 5, 3, 5, 4, 5, 5, 10, 10, 8, 8, 4
OFFSET
3,1
COMMENTS
This is the first sequence from the series of sequences: "Smallest b-a such that a < prime(n)^k < b, where a,b are semiprimes", k = 1, 2, 3, ... .
This series of sequences was inspired by Zak Seidov's message to Seqfans (Mar 02 2017) where he suggested listing the triples of primes squared with neighbor semiprimes.
There are no semiprimes below prime(2) = 3 but there are below prime(3) = 5 so the offset is 3. - David A. Corneth, Mar 04 2017
From Michael De Vlieger, Mar 04 2017: (Start)
Largest term in range a(3)..a(10^m): {7, 11, 24, 38, 54, 74, ...}.
Largest term in range a(3)..a(2^m), m>1: {3, 6, 7, 11, 11, 14, 19, 20, 24, 25, 38, 38, 38, 47, 47, 55, 70, 74, ...}.
Largest run in range a(3)..a(10^m): {2, 4, 6, 8, 10, 12, ...}.
Largest run in range a(3)..a(2^m), m>1: {1, 2, 2, 4, 4, 4, 4, 5, 6, 7, 7, 8, 8, 10, 10, 10, 12, 12, ...}. (End)
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 3..10000
FORMULA
a(n) = A102414(n) - A102415(n). - Michel Marcus, Mar 04 2017
EXAMPLE
For a(3), the largest semiprime below 5 is 4. The least semiprime above 5 is 6. Therefore, (a, b) = (4, 6) giving a(3) = 6 - 4 = 2. - David A. Corneth, Mar 04 2017
MATHEMATICA
Table[Module[{p = Prime@ n, a, b}, a = p - 1; b = p + 1; While[PrimeOmega@ a != 2, a--]; While[PrimeOmega@ b != 2, b++]; b - a], {n, 3, 120}] (* Michael De Vlieger, Mar 04 2017 *)
PROG
(PARI) issemi(n)=bigomega(n)==2
a(n, p=prime(n))=my(a=p, b=p); while(!issemi(a--), ); while(!issemi(b++), ); b-a \\ Charles R Greathouse IV, Mar 04 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Mar 04 2017
EXTENSIONS
More terms from Peter J. C. Moses, Mar 04 2017
STATUS
approved