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A251092 a(n) is the number of primes in the n-th group of consecutive primes among the odd numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..100.

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 *)

CROSSREFS

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

Sequence in context: A214609 A152159 A090341 * A175632 A226481 A088435

Adjacent sequences:  A251089 A251090 A251091 * A251093 A251094 A251095

KEYWORD

nonn

AUTHOR

Arthur Edward Chadwick, Mar 20 2015

STATUS

approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)