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A080380 Least n such that n consecutive values in A080378 equal 0; i.e., exactly n differences between consecutive primes are divisible by 4. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A039935 A090821 A226575

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

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Last modified May 29 02:00 EDT 2022. Contains 354122 sequences. (Running on oeis4.)