cp's OEIS Frontend

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.

%I A198244 #58 Nov 01 2024 20:45:32
%S A198244 11,10778947368421,17513875027111,610851724137931,614910264406779661,
%T A198244 22390512687494871811,22793803793211153712637,79905927161140977116221,
%U A198244 184251916941751188170917,319465039747605973452001,1311848376806967295019263,1918542715220370688851293
%N 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.
%C A198244 Subsequence of A060885.
%C A198244 From _Bernard Schott_, Nov 01 2019: (Start)
%C A198244 These are the primes associated with the terms k of A308238.
%C A198244 A162861 = A286301 Union {this sequence}.
%C A198244 The numbers of this sequence R_11 = 11111111111_k with k > 1 are Brazilian primes, so belong to A085104. (End)
%H A198244 Chai Wah Wu, <a href="/A198244/b198244.txt">Table of n, a(n) for n = 1..1658</a>
%H A198244 <a href="https://oeis.org/index/Br#Brazilian_numbers">Index entries for sequences related to Brazilian Numbers</a>
%F A198244 {A060885(A018252(n)) which are in A000040}.
%e A198244 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.
%p A198244 f:= proc(n)
%p A198244 local p,j;
%p A198244 if isprime(n) then return NULL fi;
%p A198244 p:= add(n^j,j=0..10);
%p A198244 if isprime(p) then p else NULL fi
%p A198244 end proc:
%p A198244 map(f, [$1..1000]); # _Robert Israel_, Nov 19 2014
%o A198244 (Python)
%o A198244 from sympy import isprime
%o A198244 A198244_list, m = [], [3628800, -15966720, 28828800, -27442800, 14707440, -4379760, 665808, -42240, 682, 0, 1]
%o A198244 for n in range(1,10**4):
%o A198244     for i in range(10):
%o A198244         m[i+1]+= m[i]
%o A198244     if not isprime(n) and isprime(m[-1]):
%o A198244         A198244_list.append(m[-1]) # _Chai Wah Wu_, Nov 09 2014
%o A198244 (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
%o A198244 (PARI) forcomposite(n=0,10^3,my(t=sum(k=0,10,n^k));if(isprime(t),print1(t,", "))); \\ _Joerg Arndt_, Nov 10 2014
%Y A198244 Cf. A162861, A000040, A088548, A192321, A102909, A060885, A308238.
%Y A198244 Similar to A185632 (k^2+ ...), A193366 (k^4+ ...), A194194 (k^6+ ...).
%K A198244 nonn
%O A198244 1,1
%A A198244 _Jonathan Vos Post_, Dec 21 2012
%E A198244 a(5)-a(6) from _Robert G. Wilson v_, Dec 21 2012
%E A198244 a(7) from _Michael B. Porter_, Dec 27 2012
%E A198244 Corrected terms a(6)-a(7) and added terms by _Chai Wah Wu_, Nov 09 2014