A251092 a(n) is the number of primes in the n-th group of consecutive primes among the odd numbers.

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

Offset: 1

Author

Arthur Edward Chadwick, Mar 20 2015

Keywords

• nonn

Comments

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.

Essentially the same as A175632. - Robert Israel, Mar 29 2015

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040 (prime numbers), A005408 (odd numbers), A001097 (twin primes), A175632.

Programs

Maple

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

Mathematica

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 *)