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.

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

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