cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A193366 Primes of the form n^4 + n^3 + n^2 + n + 1 where n is nonprime.

Original entry on oeis.org

5, 22621, 245411, 346201, 637421, 837931, 2625641, 3835261, 6377551, 15018571, 16007041, 21700501, 30397351, 35615581, 52822061, 78914411, 97039801, 147753211, 189004141, 195534851, 209102521, 223364311, 279086341, 324842131, 421106401, 445120421, 566124791, 693025471, 727832821, 745720141, 880331261, 943280801, 987082981, 1544755411, 1740422941
Offset: 1

Views

Author

Jonathan Vos Post, Dec 20 2012

Keywords

Comments

Note that there are no primes of the form n^3 + n^2 + n + 1 = (n+1)*(n^2+1) as irreducible components over Z.
From Bernard Schott, May 15 2017: (Start)
These are the primes associated with A286094.
A088548 = A190527 Union {This sequence}.
All the numbers of this sequence n^4 + n^3 + n^2 + n + 1 = 11111_n with n > 1 are Brazilian numbers, so belong to A125134 and A085104. (End)

Examples

			a(1) = 1^4 + 1^3 + 1^2 + 1 + 1 = 5.
a(2) = 12^4 + 12^3 + 12^2 + 12 + 1 = 22621.

Links

Crossrefs

Subsequence of A088548.
Cf. A000040, A018252, A185632, A192321.
Cf. A049409, A053699, A065509, A085104, A088548, A125134, A190527, A286094.

Programs

  • Maple
    for n from 1 to 150 do p(n):= 1+n+n^2+n^3+n^4;
if tau(n)>2 and isprime(p(n)) then print(n,p(n)) else fi od: # Bernard Schott, May 15 2017
  • Mathematica
    Select[Map[Total[#^Range[0, 4]] &, Select[Range@ 204, ! PrimeQ@ # &]], PrimeQ] (* Michael De Vlieger, May 15 2017 *)
  • PARI
    print1(5);forcomposite(n=4,1e3,if(isprime(t=n^4+n^3+n^2+n+1),print1(", "t))) \\ Charles R Greathouse IV, Mar 25 2013

Formula

{n^4 + n^3 + n^2 + n + 1 where n is in A018252}.

A194194 Primes of the form n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 where n is nonprime.

Original entry on oeis.org

7, 55987, 8108731, 321272407, 3092313043, 4201025641, 9684836827, 31401724537, 47446779661, 83925549247, 100343116693, 141276239497, 265462278481, 438668366137, 654022685443, 742912017121, 2333350772341, 3324554405047, 4033516174507, 4432676798593, 9752186278927, 14505760086637, 15656690128843, 16882733081761
Offset: 1

Views

Author

Jonathan Vos Post, Dec 20 2012

Keywords

Comments

Subset of A088550. The n in A018252 for which n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 are prime begin 1, 6, 14, 26, 38, 40.

Examples

			a(1) = 1^6 + 1^5 + 1^4 + 1^3 + 1^2 + 1 + 1 = 7.
a(2) = 6^6 + 6^5 + 6^4 + 6^3 + 6^2 + 6 + 1 = 55987.
a(3) = 14^6 + 14^5 + 14^4 + 14^3 + 14^2 + 14 + 1 = 8108731.
a(4) = 26^6 + 26^5 + 26^4 + 26^3 + 26^2 + 26 + 1 = 321272407.

Links

Crossrefs

Cf, A000040, A018252, A088548, A185632, A192321.

Programs

  • Mathematica
    With[{nn=200},Select[Total[#^Range[0,6]]&/@Complement[Range[nn], Prime[ Range[PrimePi[nn]]]],PrimeQ]] (* Harvey P. Dale, Nov 15 2013 *)

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

Views

Author

Jonathan Vos Post, Dec 21 2012

Keywords

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)

Examples

			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.

Links

Crossrefs

Cf. A162861, A000040, A088548, A192321, A102909, A060885, A308238.
Similar to A185632 (k^2+ ...), A193366 (k^4+ ...), A194194 (k^6+ ...).

Programs

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

Formula

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

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

A193144 Primes of the form n^2 + n + 1, where n is semiprime.

Original entry on oeis.org

43, 211, 241, 463, 1123, 1483, 3307, 3907, 4831, 6007, 12433, 14281, 20023, 20593, 24181, 26083, 37831, 41413, 42643, 43891, 46441, 47743, 77563, 82657, 95791, 98911, 108571, 145543, 156421, 158803, 200257, 205663, 239611, 284623, 288907, 304153, 307471
Offset: 1

Views

Author

Jonathan Vos Post, Dec 19 2012

Keywords

Comments

This is to semiprimes A001358 as A185632 is to nonprimes A018252.

Examples

			43 is in the sequence because it is prime, and 43 = 6^2 + 6 + 1 where 6 = 2*3 is semiprime.

Crossrefs

Cf. A000040, A001358, A185632, A192321.

Programs

  • Mathematica
    Select[#^2+#+1&/@Select[Range[1000],PrimeOmega[#]==2&],PrimeQ] (* Harvey P. Dale, Jan 06 2013 *)

Formula

{k: k is in A001358 and n^2 + n + 1 is in A000040}.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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