A367021 - OEIS

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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.

5, 10, 17, 18, 23, 26, 28, 31, 36, 39, 41, 49, 53, 58, 59, 60, 67, 68, 71, 75, 77, 78, 83, 84, 90, 95, 97, 101, 102, 109, 112, 121, 124, 127, 128, 129, 131, 132, 138, 139, 143, 150, 152, 155, 156, 158, 159, 160, 161, 162, 168, 169, 172, 173, 180, 181, 184, 187, 192

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

EXAMPLE

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.

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.

PROG

(Python)

from sympy import isprime

primes = [x for x in range(2, 3000) if isprime(x)]

comps = [x for x in range(1, 3000) if not isprime(x)]

psums = set(sum(primes[p:p+pn]) for pn in range(2, 100) for p in range(len(primes)-pn))

csums = set(sum(comps[c:c+cn]) for cn in range(2, 100) for c in range(len(comps)-cn))