A193366 -id:A193366 - cp's OEIS frontend

A286094 Nonprime numbers n such that n^4 + n^3 + n^2 + n + 1 is prime.

1, 12, 22, 24, 28, 30, 40, 44, 50, 62, 63, 68, 74, 77, 85, 94, 99, 110, 117, 118, 120, 122, 129, 134, 143, 145, 154, 162, 164, 165, 172, 175

Offset: 1

Bernard Schott, May 02 2017

nonn

A065509 Union {this sequence} = A049409.

The corresponding prime numbers n^4 + n^3 + n^2 + n + 1 = 11111_n are in A193366; these Brazilian primes, except 5 which is not Brazilian, belong to A085104 and A285017.

			12 is in the sequence because 12^4 + 12^3 + 12^2 + 12 + 1 = 11111_12 = 22621, which is prime.

R. J. Cano, Table of n, a(n) for n = 1..10000
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.

Cf. A049409, A065509, A085104, A088548, A125134, A190527, A193366, A285017.

Select[Range@ 414, And[! PrimeQ@ #, PrimeQ[Total[#^Range[0, 4]]]] &] (* Michael De Vlieger, May 03 2017 *)

isok(n)=if(n==1,5,if(ispseudoprime(n), 0, isprime(fromdigits([1, 1, 1, 1, 1], n))));
getfirstterms(n)={my(L:list, c:small); L=List(); c=0; forstep(k=1, +oo, 1, if(isok(k), listput(L, k); if(c++==n, break))); return(Vec(L))} \\ R. J. Cano, May 09 2017

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.

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Dec 21 2012

nonn

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)

			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.

Cf. A162861, A000040, A088548, A192321, A102909, A060885, A308238.

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

[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

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

forcomposite(n=0,10^3,my(t=sum(k=0,10,n^k));if(isprime(t),print1(t,", "))); \\ Joerg Arndt, Nov 10 2014

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

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

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

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A286094 Nonprime numbers n such that n^4 + n^3 + n^2 + n + 1 is prime.

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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.

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