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A080379
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Least n such that n consecutive values in A080378 equals 2; i.e. exactly n differences between consecutive primes give residues 2 when divided by 4.
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1
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5, 2, 9, 15, 39, 32, 305, 51, 2631, 3685, 170, 1156, 8775, 98, 5295, 41914, 106469, 167115, 186917, 1098776, 187784, 976193, 1166047, 423098, 77442332, 2643158, 11004239, 36330320, 259652255, 307899596, 2573725031, 411764049, 4080634008, 14841740642, 6022532018, 17035372732, 35045523209
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OFFSET
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1,1
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COMMENTS
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a(43) = 147618899630. - Donovan Johnson
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LINKS
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Table of n, a(n) for n=1..37.
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FORMULA
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a(n)=Min{x; Union[{Mod[A001223(x), 4], ..., Mod[A001223(x+n-1), 4]}]=2}
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EXAMPLE
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n=4: a(4)=15,differences between {47,53,59,61,67} are {6,6,2,6} corresponds to exactly four differences congruent to 2 mod 4,since before and after 47-43=4 or 71-67=4 are congruent to 0 mod 4.
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MATHEMATICA
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dp[x_] := Mod[Prime[x+1]-Prime[x], 4] pat[x_, h_] := Table[dp[x+j], {j, 0, h-1}] up[x_, h_] := Union[pat[x, h]] Table[fa=1; k=0; Do[s=up[n, h]; s1=Length[s]; s2=Part[u=pat[n+1, h], Length[u]]; s3=Part[w=pat[n-1, h], 1]; If[Equal[s1, 1]&&Equal[fa, 1]&&Equal[s2, 0]&&Equal[s3, 0], k=k+1; Print[{k, h, n, Prime[n], s, s1}]; fa=0], {n, 2, 200000}], {h, 1, 19}]
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CROSSREFS
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Cf. A001223, A080378, A080381.
Sequence in context: A119946 A065270 A065282 * A127098 A127097 A040024
Adjacent sequences: A080376 A080377 A080378 * A080380 A080381 A080382
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 04 2003
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EXTENSIONS
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a(20)-a(37) from Donovan Johnson, Nov 16 2010
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STATUS
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approved
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