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Search: id:A134143
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| A134143 |
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Let T(n) = (p, p+2) denote the n-th pair of twin primes. Let S(n) = 2p+2 (see A054735). Then a(n) = number of ways of writing S(n) as S(i) + S(j) with i <= j < m. |
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+0
1
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| 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 3, 1, 4, 3, 3, 3, 2, 6, 3, 5, 3, 3, 3, 3, 3, 8, 4, 2, 3, 3, 6, 4, 4, 6, 7, 8, 3, 6, 3, 9, 8, 7, 7, 5, 8, 4, 1, 6, 6, 3, 7, 1, 6, 6, 4, 8, 1, 5, 5, 8, 9, 11, 10, 6, 8, 16, 13, 9, 12, 6, 7, 8, 4, 16, 9, 6, 13, 10, 9, 5, 6, 6, 8, 11, 16, 11, 13, 6, 6, 6, 17, 9, 6, 6, 4
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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It is conjectured that a(n) > 0 for n >= 3.
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REFERENCES
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R. K. Guy, ed., Unsolved Problems, Western Number Theory Meeting, Las Vegas, 1988.
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LINKS
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Jmes A. Sellers, Table of n, a(n) for n = 1..680
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EXAMPLE
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a(4) = 1 because S(4) = 17+19 = (5+7) + (11+13) = S(2)+S(3) and this is the only such way to write S(4) as the sum S(i) + S(j) for i <= j < 4.
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MAPLE
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(Maple program from James A. Sellers) with(numtheory): Sset := {}; for i from 1 to 5000 do if ithprime(i + 1) - ithprime(i) = 2 then Sset := Sset union {2 ithprime(i) + 2} fi; od; Sset := convert(Sset, list): for n from 1 to nops(Sset) do count := 0: s := Sset[n]: for i from 1 to n do if member(s - Sset[i], Sset) and s - Sset[i] >= s/2 then count:=count + 1 fi: od: printf(`%d, `, count): od:
(Maple program from R. J. Mathar) A001359 := proc(n) option remember;
local a;
if n = 1 then
3;
else
for a from A001359(n-1)+2 by 2 do
if isprime(a) and isprime(a+2) then
RETURN(a);
fi;
od:
fi;
end:
A054735 := proc(n) option remember;
2*A001359(n)+2;
end:
A000001 := proc(n)
local Sn, i, j, a;
Sn := A054735(n);
a := 0;
for i from 1 to n-1 do
for j from i to n-1 do
if A054735(i)+A054735(j) = Sn then
a := a+1;
fi;
od:
od:
RETURN(a);
end:
for n from 1 to 120 do
# print(n, A001359(n));
#print(n, A054735(n));
#print(n, A000001(n));
printf("%d, ", A000001(n));
od:
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CROSSREFS
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Cf. A054735, A001359.
Sequence in context: A062246 A037811 A091237 this_sequence A085684 A071338 A078826
Adjacent sequences: A134140 A134141 A134142 this_sequence A134144 A134145 A134146
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KEYWORD
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nonn
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AUTHOR
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njas, Jan 25 2008
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EXTENSIONS
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Terms from a(5) onwards computed by James A. Sellers (sellersj(AT)math.psu.edu) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 25 2008
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