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A343454
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Numbers k such that k^2+2*A001414(k) and k^2-2*A001414(k) are primes.
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1
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21, 33, 35, 39, 111, 339, 473, 629, 735, 779, 795, 801, 959, 1025, 1119, 1149, 1245, 1253, 1281, 1575, 1589, 1695, 1851, 1919, 1961, 1985, 2199, 2315, 2523, 2561, 2681, 2759, 3003, 3065, 3189, 3233, 3315, 3443, 3893, 3983, 4175, 4299, 4359, 4375, 4455, 4503, 4693, 4925, 5247, 5585, 5609, 5703
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OFFSET
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1,1
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COMMENTS
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Square roots of squares in A050705.
All terms are odd.
Includes 3*p if p, 9*p^2+2*p+6 and 9*p^2-2*p-6 are all primes; the generalized Bunyakovsky conjecture implies there are infinitely many of these.
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LINKS
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EXAMPLE
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a(3) = 35 is a term because A001414(35) = 12 and 35^2-2*12 = 1201 and 35^2+2*12 = 1249 are primes.
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MAPLE
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spf:= n -> add(t[1]*t[2], t=ifactors(n)[2]):
filter:= proc(n) local s; s:= spf(n); isprime(n^2-2*s) and isprime(n^2+2*s) end proc:
select(filter, [seq(i, i=1..10000, 2)]);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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