

A080379


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.


1



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

1,1


COMMENTS

a(43) = 147618899630.  Donovan Johnson


LINKS

Table of n, a(n) for n=1..37.


FORMULA

a(n)=Min{x; Union[{Mod[A001223(x), 4], ..., Mod[A001223(x+n1), 4]}]=2}


EXAMPLE

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 4743=4 or 7167=4 are congruent to 0 mod 4.


MATHEMATICA

dp[x_] := Mod[Prime[x+1]Prime[x], 4] pat[x_, h_] := Table[dp[x+j], {j, 0, h1}] 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[n1, 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}]


CROSSREFS

Cf. A001223, A080378, A080381.
Sequence in context: A119946 A065270 A065282 * A257513 A127098 A127097
Adjacent sequences: A080376 A080377 A080378 * A080380 A080381 A080382


KEYWORD

nonn


AUTHOR

Labos Elemer, Mar 04 2003


EXTENSIONS

a(20)a(37) from Donovan Johnson, Nov 16 2010


STATUS

approved



