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A251092
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a(n) is the number of primes in the n-th group of consecutive primes among the odd numbers.
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2
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3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,1
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COMMENTS
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Explanation:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25,... = Odd numbers
^ ^ ^ ^ ^ ^ ^ ^ = Prime numbers
<---3---> <--2--> <--2--> <-1-> = Primes beside other primes divided into groups of how many there are.
Note that the first group (3, 5 and 7) is the only group of 3. Therefore the rest of the sequence only consists of 1's and 2's.
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LINKS
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MAPLE
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N:= 1000: # to use the first N+1 odd numbers
L:= map(t -> isprime(2*t+1), [$1..N]):
Starts:= [1, op(select(i -> L[i] and not L[i-1], [$2..N]))]:
Ends:= select(i -> L[i] and not L[i+1], [$1..N-1]):
seq(Ends[i]-Starts[i]+1, i=1..nops(Ends)); # Robert Israel, Mar 27 2015
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MATHEMATICA
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Length /@ Split[Select[2 Range@ 1200 - 1, PrimeQ], #2 - #1 == 2 &] (* Michael De Vlieger, Mar 20 2015 *)
Length/@DeleteCases[Split[Table[If[PrimeQ[n], 1, 0], {n, 3, 1001, 2}]], _?(FreeQ[ #, 1]&)] (* Harvey P. Dale, Jun 29 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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