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A198244
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Primes of the form k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 where k is nonprime.
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2
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11, 10778947368421, 17513875027111, 610851724137931, 614910264406779661, 22390512687494871811, 22793803793211153712637, 79905927161140977116221, 184251916941751188170917, 319465039747605973452001, 1311848376806967295019263, 1918542715220370688851293
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OFFSET
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1,1
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COMMENTS
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These are the primes associated with the terms k of A308238.
The numbers of this sequence R_11 = 11111111111_k with k > 1 are Brazilian primes, so belong to A085104. (End)
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LINKS
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FORMULA
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EXAMPLE
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10778947368421 is in the sequence since 10778947368421 = 20^10 + 20^9 + 20^8 + 20^7 + 20^6 + 20^5 + 20^4 + 20^3 + 20^2 + 20 + 1, 20 is not prime, and 10778947368421 is prime.
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MAPLE
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f:= proc(n)
local p, j;
if isprime(n) then return NULL fi;
p:= add(n^j, j=0..10);
if isprime(p) then p else NULL fi
end proc:
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PROG
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(Python)
from sympy import isprime
A198244_list, m = [], [3628800, -15966720, 28828800, -27442800, 14707440, -4379760, 665808, -42240, 682, 0, 1]
for n in range(1, 10**4):
....for i in range(10):
........m[i+1]+= m[i]
....if not isprime(n) and isprime(m[-1]):
(Magma) [a: n in [0..500] | not IsPrime(n) and IsPrime(a) where a is (n^10+n^9+n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1)]; // Vincenzo Librandi, Nov 09 2014
(PARI) forcomposite(n=0, 10^3, my(t=sum(k=0, 10, n^k)); if(isprime(t), print1(t, ", "))); \\ Joerg Arndt, Nov 10 2014
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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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Corrected terms a(6)-a(7) and added terms by Chai Wah Wu, Nov 09 2014
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STATUS
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approved
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