A198244 - OEIS

%I #58 Nov 01 2024 20:45:32

%S 11,10778947368421,17513875027111,610851724137931,614910264406779661,

%T 22390512687494871811,22793803793211153712637,79905927161140977116221,

%U 184251916941751188170917,319465039747605973452001,1311848376806967295019263,1918542715220370688851293

%N 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 Subsequence of A060885.

%C From _Bernard Schott_, Nov 01 2019: (Start)

%C These are the primes associated with the terms k of A308238.

%C A162861 = A286301 Union {this sequence}.

%C The numbers of this sequence R_11 = 11111111111_k with k > 1 are Brazilian primes, so belong to A085104. (End)

%H Chai Wah Wu, <a href="/A198244/b198244.txt">Table of n, a(n) for n = 1..1658</a>

%H <a href="https://oeis.org/index/Br#Brazilian_numbers">Index entries for sequences related to Brazilian Numbers</a>

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

%e 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 f:= proc(n)

%p local p,j;

%p if isprime(n) then return NULL fi;

%p p:= add(n^j,j=0..10);

%p if isprime(p) then p else NULL fi

%p end proc:

%p map(f, [$1..1000]); # _Robert Israel_, Nov 19 2014

%o (Python)

%o from sympy import isprime

%o A198244_list, m = [], [3628800, -15966720, 28828800, -27442800, 14707440, -4379760, 665808, -42240, 682, 0, 1]

%o for n in range(1,10**4):

%o     for i in range(10):

%o         m[i+1]+= m[i]

%o     if not isprime(n) and isprime(m[-1]):

%o         A198244_list.append(m[-1]) # _Chai Wah Wu_, Nov 09 2014

%o (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 (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 Cf. A162861, A000040, A088548, A192321, A102909, A060885, A308238.

%Y Similar to A185632 (k^2+ ...), A193366 (k^4+ ...), A194194 (k^6+ ...).

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Dec 21 2012

%E a(5)-a(6) from _Robert G. Wilson v_, Dec 21 2012

%E a(7) from _Michael B. Porter_, Dec 27 2012

%E Corrected terms a(6)-a(7) and added terms by _Chai Wah Wu_, Nov 09 2014