A080380 Least n such that n consecutive values in A080378 equal 0; i.e., exactly n differences between consecutive primes are divisible by 4.

4, 24, 46, 153, 1480, 90, 3875, 1395, 16591, 61457, 240748, 21355, 772038, 613491, 804584, 6067263, 16791134, 16138563, 37593808, 250379098, 73857828, 124789332, 56307979, 3295708683, 3511121443, 27497699943, 64430269615, 26284355567, 118413975572, 225822728018, 4645422093, 118027458557

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Example

n=2: a(2)=24, p(24)=89, followed by {4, 4} consecutive prime differences, surrounded by 6=89-83 and 2=103-101 also as p-differences, both congruent to 2 modulo 4.

Mathematica

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[s, {0}]&&Equal[fa, 1]&&Equal[s2, 2]&&Equal[s3, 2], k=k+1; Print[{k, h, n, Prime[n], s, s1}]; fa=0], {n, 2, 720000}], {h, 1, 14}]

Crossrefs

Cf. A001223, A080378, A080379.

Sequence in context: A139245 A224242 A066770 * A364278 A039935 A090821

Adjacent sequences: A080377 A080378 A080379 * A080381 A080382 A080383

Keyword

nonn

Author

Labos Elemer, Mar 06 2003

Extensions

a(15)-a(32) from Donovan Johnson, Nov 16 2010

Status

approved