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A082074 One quarter of first differences of primes with 4k+1 form, A002144. 1
2, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 6, 3, 2, 4, 2, 3, 1, 8, 1, 2, 4, 3, 2, 1, 3, 5, 1, 5, 3, 1, 5, 4, 2, 1, 2, 3, 3, 4, 2, 1, 12, 3, 5, 4, 3, 2, 4, 2, 3, 1, 6, 3, 2, 3, 1, 6, 2, 6, 6, 1, 2, 1, 6, 3, 3, 2, 6, 1, 5, 1, 12, 2, 1, 3, 6, 5, 3, 1, 2, 3, 4, 3, 2, 6, 1, 3, 2, 3, 6, 7, 3, 2, 3, 1, 3, 2, 3, 7, 3, 2, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

FORMULA

a(n)=[A002144(n+1)-A002144(n)]/4

EXAMPLE

first and second 4k+1 primes are 5 and 13, so a(1)=(13-5)/4=2;

MATHEMATICA

k=0; m=4; r=1; 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[4*Range[1000]+1, PrimeQ]]/4 (* Harvey P. Dale, Dec 04 2011 *)

CROSSREFS

Cf. A002144, A002145, A082073-A082076.

Sequence in context: A194859 A194838 A085014 * A132283 A307081 A256440

Adjacent sequences:  A082071 A082072 A082073 * A082075 A082076 A082077

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 07 2003

STATUS

approved

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Last modified May 28 12:32 EDT 2020. Contains 334681 sequences. (Running on oeis4.)