cp's OEIS Frontend

A367021 Numbers that can be written as both the sum of two or more consecutive nonprimes and the sum of two or more consecutive primes.

%I A367021 #37 Dec 31 2023 00:12:45
%S A367021 5,10,17,18,23,26,28,31,36,39,41,49,53,58,59,60,67,68,71,75,77,78,83,
%T A367021 84,90,95,97,101,102,109,112,121,124,127,128,129,131,132,138,139,143,
%U A367021 150,152,155,156,158,159,160,161,162,168,169,172,173,180,181,184,187,192
%N A367021 Numbers that can be written as both the sum of two or more consecutive nonprimes and the sum of two or more consecutive primes.
%C A367021 It seems that more than one consecutive number set from one kind or the other may exist for a term. Also, for some terms, an equal number of addends from each kind may correspond.
%H A367021 David Consiglio, Jr., <a href="/A367021/b367021.txt">Table of n, a(n) for n = 1..1000</a>
%e A367021 5 is a term because 5 = 1 + 4 = 2 + 3, which is the sum of two consecutive nonprimes and also the sum of two consecutive primes.
%e A367021 17 is a term because 17 = 8 + 9 = 2 + 3 + 5 + 7, the sum of two consecutive nonprimes and also the sum of four consecutive primes.
%o A367021 (Python)
%o A367021 from sympy import isprime
%o A367021 primes = [x for x in range(2,3000) if isprime(x)]
%o A367021 comps = [x for x in range(1,3000) if not isprime(x)]
%o A367021 psums = set(sum(primes[p:p+pn]) for pn in range(2,100) for p in range(len(primes)-pn))
%o A367021 csums = set(sum(comps[c:c+cn]) for cn in range(2,100) for c in range(len(comps)-cn))
%o A367021 terms = sorted(list(psums.intersection(csums)))
%o A367021 print(terms)
%o A367021 # _David Consiglio, Jr._, Dec 18 2023
%Y A367021 Cf. A018252, A050936, A366976.
%K A367021 nonn
%O A367021 1,1
%A A367021 _Tamas Sandor Nagy_, Nov 01 2023
%E A367021 More terms from _David Consiglio, Jr._, Dec 18 2023