Search: a277730 -id:a277730
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A277729
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Irregular triangle read by rows: T(n,k) = number of times a gap of k occurs between the first n successive primes.
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+10
2
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1, 1, 1, 1, 2, 1, 2, 0, 1, 1, 3, 0, 1, 1, 3, 0, 2, 1, 4, 0, 2, 1, 4, 0, 3, 1, 4, 0, 3, 0, 1, 1, 5, 0, 3, 0, 1, 1, 5, 0, 3, 0, 2, 1, 5, 0, 4, 0, 2, 1, 6, 0, 4, 0, 2, 1, 6, 0, 5, 0, 2, 1, 6, 0, 5, 0, 3, 1, 6, 0, 5, 0, 4, 1, 7, 0, 5, 0, 4, 1, 7, 0, 5, 0, 5, 1, 7, 0, 6, 0, 5, 1, 8, 0, 6, 0, 5, 1, 8, 0, 6, 0, 6, 1, 8, 0, 7, 0, 6, 1, 8, 0, 7, 0, 7, 1, 8, 0, 7, 0, 7, 0, 1, 1, 8, 0, 8, 0, 7, 0, 1, 1, 9, 0
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OFFSET
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2,5
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LINKS
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EXAMPLE
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Triangle begins:
1,
1, 1,
1, 2,
1, 2, 0, 1,
1, 3, 0, 1, <- gaps in 2,3,5,7,11,13 are 1, 2 (3 times), 4 (once)
1, 3, 0, 2,
1, 4, 0, 2,
1, 4, 0, 3,
1, 4, 0, 3, 0, 1,
1, 5, 0, 3, 0, 1,
1, 5, 0, 3, 0, 2,
1, 5, 0, 4, 0, 2,
1, 6, 0, 4, 0, 2,
1, 6, 0, 5, 0, 2,
1, 6, 0, 5, 0, 3,
1, 6, 0, 5, 0, 4,
1, 7, 0, 5, 0, 4,
1, 7, 0, 5, 0, 5,
1, 7, 0, 6, 0, 5,
1, 8, 0, 6, 0, 5,
...
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MAPLE
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N:= 30: # for rows 2 to N
res:= 1; p:= 3; R:= <1>;
for n from 2 to N do
pp:= nextprime(p);
d:= pp - p;
p:= pp;
if d <= LinearAlgebra:-Dimension(R) then
R[d]:= R[d]+1
else
R(d):= 1
fi;
res:= res, op(convert(R, list));
od:
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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