A205901 Number of primes between two consecutive primes of the form n^2 + 1.

1, 3, 4, 13, 18, 9, 23, 26, 16, 87, 40, 169, 23, 148, 127, 183, 111, 81, 346, 146, 91, 109, 51, 99, 108, 334, 122, 186, 115, 326, 192, 137, 148, 726, 83, 152, 562, 244, 254, 182, 439, 266, 192, 174, 295, 487, 196, 821, 327, 424, 660, 793, 600, 2108, 124, 663

Offset

1,2

Comments

a(n) = number of primes between A002496(n) and A002496(n+1).

Conjecture: this sequence is infinite, because it is conjectured that the sequence A002496 is infinite, although this has never been proved.

Links

Michel Lagneau, Table of n, a(n) for n = 1..1000

Example

a(4) = 13 because A002496(4) = 37, A002496(5)=101 and the 13 primes between 37 and 101 are {41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.

Maple

T:=array(1..900): T[1]:=2:ii:=1:for x from 2 by 2 to 10000 do:y:=x^2+1:if type(y, prime)=true then ii:=ii+1:T[ii]:=y:else fi:od:for k from 1 to ii-1do: p0:=T[k]:p1:= T[k+1]: j:=0:for m from p0+1 to p1-1 do:if type(m, prime)=true then j:=j+1:else fi:od:  printf(`%d, `, j):od:

Crossrefs

Cf. A002496.

Sequence in context: A023857 A323149 A291250 * A302392 A293941 A182691

Adjacent sequences: A205898 A205899 A205900 * A205902 A205903 A205904

Keyword

nonn

Author

Michel Lagneau, Feb 01 2012

Status

approved