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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 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, !PrimeQ[ # ] && !PrimeQ[2#-1] &] Select[Range, 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 A096229 A231718 Adjacent sequences:  A138663 A138664 A138665 * A138667 A138668 A138669 KEYWORD nice,nonn AUTHOR T. D. Noe, Mar 26 2008 STATUS approved

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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)