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A082076
First differences of primes of the form 4*k+3 (A002145), divided by 4.
6
1, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 1, 5, 1, 5, 1, 2, 3, 3, 1, 3, 3, 2, 3, 3, 1, 3, 3, 3, 2, 3, 6, 1, 5, 4, 3, 2, 3, 1, 9, 3, 2, 1, 5, 1, 3, 2, 1, 2, 1, 5, 6, 4, 2, 4, 3, 2, 3, 3, 3, 1, 3, 6, 2, 7, 2, 3, 1, 2, 9, 6, 3, 1, 3, 5, 1, 5, 1, 5, 1, 2, 7, 5, 1, 3, 2, 7, 3, 2, 3, 3, 6, 1, 3, 5, 7, 3, 2, 4, 9, 2, 7, 5, 1, 2
OFFSET
1,3
LINKS
FORMULA
a(n) = (A002145(n+1) - A002145(n))/4.
EXAMPLE
The first and second primes of the form 4*k+3 are 3 and 7, so a(1) = (7-3)/4 = 1.
MATHEMATICA
k=0; m=4; r=3; Do[s=Mod[Prime[n], m]; If[Equal[s, r], rp=ep; k=k+1; ep=Prime[n]; Print[(ep-rp)/4]; ], {n, 1, 1000}]
Differences[Select[Prime[Range[400]], IntegerQ[(#-3)/4]&]]/4 (* Harvey P. Dale, Apr 29 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 07 2003
STATUS
approved