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A138666
Numbers n such that every sum of consecutive positive numbers ending in n is not prime.
5
1, 8, 14, 18, 20, 25, 26, 28, 32, 33, 35, 38, 39, 44, 46, 48, 50, 56, 58, 60, 62, 63, 65, 68, 72, 74, 77, 78, 80, 81, 85, 86, 88, 92, 93, 94, 95, 98, 102, 104, 105, 108, 110, 111, 116, 118, 119, 122, 123, 124, 125, 128, 130, 133, 134, 138, 140, 143, 144, 145, 146, 148
OFFSET
1,2
COMMENTS
Also numbers n such that all terms in row n of A087401 are not prime. Also the index of the triangular numbers in A076768. See A087572 for the least prime, if it exists. David Wasserman points out (in A087572) that n is in this sequence if and only if n and 2n-1 are both not prime. This sequence is infinite because 2k^2 is a term for all k>1.
EXAMPLE
8 is in this sequence because 8, 15=7+8, 21=6+7+8, 26=5+6+7+8, 30=4+5+6+7+8, 33=3+4+5+6+7+8, 35=2+3+4+5+6+7+8 and 36=1+2+3+4+5+6+7+8 are all composite.
MATHEMATICA
Select[Range[200], !PrimeQ[ # ] && !PrimeQ[2#-1] &]
Select[Range[150], AllTrue[Accumulate[Reverse[Range[#]]], !PrimeQ[#]&]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 18 2017 *)
PROG
(Haskell)
a138666 n = a138666_list !! (n-1)
a138666_list = map (head . tail) $
filter (all (== 0) . map a010051 . tail) $ drop 2 a087401_tabl
-- Reinhard Zumkeller, Oct 03 2012
(Python)
from sympy import isprime
from itertools import accumulate
def ok(n): return all(not isprime(s) for s in accumulate(range(n, 0, -1)))
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(148)) # Michael S. Branicky, Jan 08 2021
CROSSREFS
Cf. A010051.
Sequence in context: A349081 A192045 A084021 * A072835 A367035 A096229
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Mar 26 2008
STATUS
approved