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

%I A318157 #28 Jan 02 2019 21:53:54
%S A318157 101,103,107,137,139,197,199,223,227,257,307,347,367,373,379,461,463,
%T A318157 467,479,487,491,499,569,571,577,587,613,617,619,641,643,677,683,701,
%U A318157 733,739,743,751,809,811,821,823,827,829,853,857,859,863,877,881,883,941
%N A318157 Primes that are one more or one less than the sum of four consecutive composite numbers.
%H A318157 Chai Wah Wu, <a href="/A318157/b318157.txt">Table of n, a(n) for n = 1..10000</a>
%e A318157 24 + 25 + 26 + 27 - 1 = 101;
%e A318157 24 + 25 + 26 + 27 + 1 = 103;
%e A318157 25 + 26 + 27 + 28 + 1 = 107.
%e A318157 26 + 27 + 28 + 29 - 1 = 109, but 29 is not composite, so 109 is not in the sequence.
%t A318157 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 *)
%o A318157 (Python)
%o A318157 from sympy import isprime
%o A318157 A318157_list = []
%o A318157 for n in range(2,10**6):
%o A318157     if not (isprime(n) or isprime(n+1) or isprime(n+2) or isprime(n+3)):
%o A318157         if isprime(4*n+5):
%o A318157             A318157_list.append(4*n+5)
%o A318157         if isprime(4*n+7):
%o A318157             A318157_list.append(4*n+7) # _Chai Wah Wu_, Jan 02 2019
%Y A318157 Cf. A296012.
%K A318157 nonn
%O A318157 1,1
%A A318157 _Martin Michael Musatov_, Aug 19 2018
%E A318157 a(16)-a(52) from _Jon E. Schoenfield_, Aug 19 2018