

A198244


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.


2



11, 10778947368421, 17513875027111, 610851724137931, 614910264406779661, 22390512687494871811, 22793803793211153712637, 79905927161140977116221, 184251916941751188170917, 319465039747605973452001, 1311848376806967295019263, 1918542715220370688851293
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OFFSET

1,1


COMMENTS

Subsequence of A060885.
From Bernard Schott, Nov 01 2019: (Start)
These are the primes associated with the terms k of A308238.
A162861 = A286301 Union {this sequence}.
The numbers of this sequence R_11 = 11111111111_k with k > 1 are Brazilian primes, so belong to A085104. (End)


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1658
Index entries for sequences related to Brazilian Numbers


FORMULA

{A060885(A018252(n)) which are in A000040}.


EXAMPLE

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.


MAPLE

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:
map(f, [$1..1000]); # Robert Israel, Nov 19 2014


PROG

(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]):
........A198244_list.append(m[1]) # Chai Wah Wu, Nov 09 2014
(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


CROSSREFS

Cf. A162861, A000040, A088548, A192321, A102909, A060885, A308238.
Similar to A185632 (k^2+ ...), A193366 (k^4+ ...), A194194 (k^6+ ...).
Sequence in context: A213647 A072218 A046844 * A066953 A213645 A257139
Adjacent sequences: A198241 A198242 A198243 * A198245 A198246 A198247


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Dec 21 2012


EXTENSIONS

a(5)a(6) from Robert G. Wilson v, Dec 21 2012
a(7) from Michael B. Porter, Dec 27 2012
Corrected terms a(6)a(7) and added terms by Chai Wah Wu, Nov 09 2014


STATUS

approved



