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

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`%I #14 Aug 20 2017 22:48:00
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`%S 1,3,4,13,18,9,23,26,16,87,40,169,23,148,127,183,111,81,346,146,91,
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`%T 109,51,99,108,334,122,186,115,326,192,137,148,726,83,152,562,244,254,
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`%U 182,439,266,192,174,295,487,196,821,327,424,660,793,600,2108,124,663
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`%N Number of primes between two consecutive primes of the form n^2 + 1.
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`%C a(n) = number of primes between A002496(n) and A002496(n+1).
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`%C Conjecture: this sequence is infinite, because it is conjectured that the sequence A002496 is infinite, although this has never been proved.
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`%H Michel Lagneau, <a href="/A205901/b205901.txt">Table of n, a(n) for n = 1..1000</a>
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`%e 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}.
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`%p 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:
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`%Y Cf. A002496.
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`%K nonn
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`%O 1,2
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`%A _Michel Lagneau_, Feb 01 2012
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