A318157 Primes that are one more or one less than the sum of four consecutive composite numbers.

101, 103, 107, 137, 139, 197, 199, 223, 227, 257, 307, 347, 367, 373, 379, 461, 463, 467, 479, 487, 491, 499, 569, 571, 577, 587, 613, 617, 619, 641, 643, 677, 683, 701, 733, 739, 743, 751, 809, 811, 821, 823, 827, 829, 853, 857, 859, 863, 877, 881, 883, 941

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

24 + 25 + 26 + 27 - 1 = 101;
24 + 25 + 26 + 27 + 1 = 103;
25 + 26 + 27 + 28 + 1 = 107.
26 + 27 + 28 + 29 - 1 = 109, but 29 is not composite, so 109 is not in the sequence.

Mathematica

tempList = Table[(Plus@@Range[n, n + 3]) * KroneckerDelta[PrimePi[n - 1], PrimePi[n + 3]], {n, 250}]; Union[Select[tempList - 1, PrimeQ], Select[tempList + 1, PrimeQ]] (* Alonso del Arte, Sep 02 2018 *)

Prog

(Python)
from sympy import isprime
A318157_list = []
for n in range(2, 10**6):
    if not (isprime(n) or isprime(n+1) or isprime(n+2) or isprime(n+3)):
        if isprime(4*n+5):
            A318157_list.append(4*n+5)
        if isprime(4*n+7):
            A318157_list.append(4*n+7) # Chai Wah Wu, Jan 02 2019

Crossrefs

Cf. A296012.

Sequence in context: A329737 A166571 A201965 * A117837 A176929 A330563

Adjacent sequences: A318154 A318155 A318156 * A318158 A318159 A318160

Keyword

nonn

Author

Martin Michael Musatov, Aug 19 2018

Extensions

a(16)-a(52) from Jon E. Schoenfield, Aug 19 2018

Status

approved