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A261542
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Integers k such that k^2 + 1 = 2*p where p and p+2 are twin primes.
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1
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3, 9, 51, 69, 231, 279, 309, 471, 519, 579, 639, 699, 819, 861, 909, 1029, 1311, 1419, 1629, 1701, 1749, 1899, 2151, 2541, 2619, 2799, 3201, 3291, 3429, 3501, 3981, 4089, 4719, 4809, 4941, 5061, 5301, 5571, 5679, 5739, 5859, 6369, 6621, 6789, 6939, 7071, 7149
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OFFSET
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1,1
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COMMENTS
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The corresponding primes p are 5, 41, 1301, 2381, 26681, 38921, 47741, 110921, 134681, ... and are in A001359 (lesser of twin primes).
Property of the sequence: the primes p > 5 are congruent to 41 mod 180 => a(n)^2 == 9, 81 mod 180 for n>1.
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LINKS
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EXAMPLE
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3 is in the sequence because 3^2 + 1 = 2*5 and 2 + 5 = 7 is prime.
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MAPLE
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with(numtheory):
for n from 1 by 2 to 8000 do:
p:=n^2+1:
if isprime(p/2) and isprime(p/2+2)
then
printf(`%d, `, n):
else
fi:
od:
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MATHEMATICA
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Select[Range[7500], AllTrue[(#^2+1)/2+{0, 2}, PrimeQ]&] (* Harvey P. Dale, Apr 09 2023 *)
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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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