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A285887
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Primes of the form (1 + x)^y + (-x)^y where y is a divisor of x.
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4
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13, 37, 41, 127, 271, 313, 421, 881, 1013, 1201, 1801, 1861, 2113, 2269, 2381, 2791, 3613, 4651, 5101, 5419, 6211, 7057, 7321, 9941, 10513, 10657, 12097, 13267, 13613, 14281, 16381, 19927, 20201, 21013, 21841, 24421, 24571, 26227, 30013, 33391, 34061, 35317, 41761, 45757, 47741, 49297
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OFFSET
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1,1
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COMMENTS
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If x = y then: 13, 37, 881, 4651, 1273609, ...
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LINKS
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EXAMPLE
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13 is in this sequence because (1 + 2)^2 + (-2)^2 = 13 is prime where 2 is divisor of 2.
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MAPLE
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N:= 100000: # To get terms <= N
Res:= NULL:
for y from 2 while 2^y -1 <= N do
z:= y/2^padic:-ordp(y, 2);
if z > 1 and (z <> y or not isprime(z)) then next fi;
for x from y by y do
v:= (1+x)^y + (-x)^y;
if v > N then break fi;
if isprime(v) then Res:= Res, v; fi
od od:
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MATHEMATICA
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Union@ Flatten@ Table[Select[Map[(1 + n)^# + (-n)^# &, Divisors@ n], PrimeQ], {n, 200}] (* Michael De Vlieger, Apr 29 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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