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A082073
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First difference set of primes with 4k+1 form: A002144.
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10
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8, 4, 12, 8, 4, 12, 8, 12, 16, 8, 4, 8, 4, 24, 12, 8, 16, 8, 12, 4, 32, 4, 8, 16, 12, 8, 4, 12, 20, 4, 20, 12, 4, 20, 16, 8, 4, 8, 12, 12, 16, 8, 4, 48, 12, 20, 16, 12, 8, 16, 8, 12, 4, 24, 12, 8, 12, 4, 24, 8, 24, 24, 4, 8, 4, 24, 12, 12, 8, 24, 4, 20, 4, 48, 8, 4, 12, 24, 20, 12, 4, 8, 12
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OFFSET
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1,1
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COMMENTS
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a(n) is divisible by 4, for all n.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A002144(n+1) - A002144(n).
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EXAMPLE
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first and second 4k+1 primes are 5 and 13, so a(1)=13-5=8;
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MATHEMATICA
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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)]; ], {n, 1, 1000}]
Differences[Select[Prime[Range[200]], Mod[#, 4]==1&]] (* Harvey P. Dale, Feb 05 2020 *)
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PROG
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(PARI) p=5; forprime(q=7, 1e3, if(q%4==1, print1(q-p", "); p=q)) \\ Charles R Greathouse IV, May 13 2012
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CROSSREFS
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Cf. A002144, A002145, A082074, A082075, A082076.
Sequence in context: A194184 A194217 A239971 * A244209 A156279 A203072
Adjacent sequences: A082070 A082071 A082072 * A082074 A082075 A082076
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KEYWORD
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nonn,easy
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AUTHOR
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Labos Elemer, Apr 07 2003
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STATUS
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approved
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