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
Keywords
Examples
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.
Programs
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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}]
Extensions
a(15)-a(32) from Donovan Johnson, Nov 16 2010