A167610 Primes that are the sum of three consecutive nonprimes.

5, 11, 23, 31, 41, 59, 67, 71, 109, 113, 131, 139, 157, 199, 211, 239, 251, 269, 293, 311, 337, 379, 383, 409, 419, 487, 491, 499, 503, 521, 571, 599, 631, 701, 751, 769, 773, 787, 829, 877, 881, 919, 941, 953, 991, 1009, 1013, 1039, 1049, 1061, 1103, 1117

Offset

1,1

Comments

Apart from 5 and 11, primes of the form 6*k - 1 where 2*k - 1 is prime while 2*k + 1 is composite, and primes of the form 6*k + 1 where 2*k + 1 is prime while 2*k - 1 is composite. - Robert Israel, Jan 23 2024

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1)=0(1st nonprime)+1(2nd nonprime)+4(3rd nonprime)=5(prime);
a(2)=1(2nd nonprime)+4(3rd nonprime)+6(4th nonprime)=11(prime);
a(3)=6(4th nonprime)+8(5th nonprime)+9(6th nonprime)=23(prime).

Maple

NP:= remove(isprime, [$0..1000]):
select(isprime, NP[1..-3] + NP[2..-2] + NP[3..-1]); # Robert Israel, Jan 23 2024

Mathematica

fn[m_]:=ResourceFunction["Composite"][m]+ResourceFunction["Composite"][m+1]+ResourceFunction["Composite"][m+2]; Join[{5, 11}, Select[Table[fn[m], {m, 300}], PrimeQ]] (* James C. McMahon, Jan 23 2024 *)

Prog

(Python)
from sympy import isprime
A167610, complist = [], [0, 1, 4]
while len(A167610) < 52:
    if isprime(totest:= sum(complist)): A167610.append(totest)
    complist.append(complist[-1]+1)
    complist = complist[1:]
    if isprime(complist[-1]): complist[-1] += 1
print(A167610) # Karl-Heinz Hofmann, Jan 24 2024

Crossrefs

Cf. A000040, A141468.

Sequence in context: A161896 A317909 A304372 * A295149 A143127 A235386

Adjacent sequences: A167607 A167608 A167609 * A167611 A167612 A167613

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 07 2009

Extensions

Corrected (47 replaced by 59, 71 inserted, 619 removed) by R. J. Mathar, May 30 2010

Status

approved