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A187828
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Partition the sequence of consecutive primes into groups so that the absolute value of the alternating sum (-1)^n (An) with n = 0,....m in each group is prime.
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1
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3, 19, 37, 53, 71, 109, 149, 211, 251, 277, 307, 359, 397, 449, 479, 521, 593, 641, 709, 769, 823, 859, 919, 1009, 1033, 1087, 1171, 1217, 1277, 1321, 1367, 1399, 1459, 1549, 1609, 1637, 1693, 1747, 1879, 1973, 2039, 2099, 2213, 2341, 2399, 2437, 2531, 2663, 2777, 2879, 2939, 3061, 3251, 3433
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OFFSET
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1,1
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COMMENTS
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From Robert Israel, Jun 24 2020: (Start)
The alternating sum must consist of more than two terms, and a(n) is the absolute value of that alternating sum.
Is the sequence increasing? For k <= 99999, a(k+1) >= a(k)+14. (End)
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(x) = Sum_{(-1)^n (An) with n = (0, 1, 2..m)}.
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EXAMPLE
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a(1)=3 because the absolute value of the alternating sum (-1)^n (An) where An = (2, 3, 5, 7) with n = (0,1,2,3), is prime; a(2)=19 because the absolute value of the alternating sum (-1)^n (An) where An = (11, 13, 17, 19, 23) with n = (0, 1, 2, 3), is prime; a(3)=37 because the absolute value of the alternating sum (-1)^n (An) where An = (29, 31, 37, 41, 43) with n = (0, 1, 2, 3, 4) is prime.
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MAPLE
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p:= 1: R:= NULL:
for count from 1 to 50 do
q:= nextprime(p); p:= nextprime(q); t:= q-p;
e:= 1;
do p:= nextprime(p);
t:= t + e*p;
e:= -e;
until isprime(abs(t));
R:= R, abs(t);
od:
R; # Robert Israel, Jun 23 2020
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CROSSREFS
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Sequence in context: A062291 A106082 A283714 * A088786 A147237 A117674
Adjacent sequences: A187825 A187826 A187827 * A187829 A187830 A187831
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KEYWORD
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nonn
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AUTHOR
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Fabio Mercurio, Dec 27 2012
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EXTENSIONS
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More terms from Robert Israel, Jun 24 2020
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STATUS
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approved
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