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 A053726 "Flag numbers": number of dots that can be arranged in successive rows of K, K-1, K, K-1, K, ..., K-1, K (assuming there is a total of L > 1 rows of size K > 1). 11
 5, 8, 11, 13, 14, 17, 18, 20, 23, 25, 26, 28, 29, 32, 33, 35, 38, 39, 41, 43, 44, 46, 47, 48, 50, 53, 56, 58, 59, 60, 61, 62, 63, 65, 67, 68, 71, 72, 73, 74, 77, 78, 80, 81, 83, 85, 86, 88, 89, 92, 93, 94, 95, 98, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 116 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers of the form F(K, L) = KL+(K-1)(L-1), K, L > 1, i.e. 2KL - (K+L) + 1, sorted and duplicates removed. If K=1, L=1 were allowed, this would contain all positive integers. Positive numbers > 1 but not of the form (odd primes plus one)/2. - Douglas Winston (douglas.winston(AT)srupc.com), Sep 11 2003 In other words, numbers n such that 2n-1, or equally, A064216(n) is a composite number. - Antti Karttunen, Apr 17 2015 Note: the following comment was originally applied in error to the numerically similar A246371. - Allan C. Wechsler, Aug 01 2022 From Matthijs Coster, Dec 22 2014: (Start) Also area of (over 45 degree) rotated rectangles with sides > 1. The area of such rectangles is 2ab - a - b + 1 = 1/2((2a-1)(2b-1)+1). Example: Here a = 3 and b = 5. The area = 23. * *** ***** ***** ***** *** * (End) LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A008508(n) + n + 1. From Antti Karttunen, Apr 17 2015: (Start) a(n) = n + A000720(A071904(n)). [The above formula reduces to this. A000720(k) gives number of primes <= k, and A071904 gives the n-th odd composite number.] a(n) = A104275(n+1). (End) PROG (Scheme, with Antti Karttunen's IntSeq-library, two alternatives) (define A053726 (MATCHING-POS 1 1 (lambda (n) (and (> n 1) (not (prime? (+ n n -1))))))) (define (A053726 n) (+ n (A000720 (A071904 n)))) ;; Antti Karttunen, Apr 17 2015 (Python) from sympy import isprime def ok(n): return n > 1 and not isprime(2*n-1) print(list(filter(ok, range(1, 117)))) # Michael S. Branicky, May 08 2021 (PARI) select( {is_A053726(n)=n>4 && !isprime(n*2-1)}, [1..115]) \\ M. F. Hasler, Aug 02 2022 CROSSREFS Essentially same as A104275, but without the initial one. A144650 sorted into ascending order, with duplicates removes. Cf. A006254 (complement, apart from 1, which is in neither sequence). Cf. also A000720, A008508, A064216, A071904, A199593, A250474. Differs from its subsequence A246371 for the first time at a(8) = 20, which is missing from A246371. Sequence in context: A047700 A294675 A104275 * A246371 A274939 A173977 Adjacent sequences: A053723 A053724 A053725 * A053727 A053728 A053729 KEYWORD nonn,easy AUTHOR Dan Asimov, asimovd(AT)aol.com, Apr 09 2003 EXTENSIONS More terms from Douglas Winston (douglas.winston(AT)srupc.com), Sep 11 2003 STATUS approved

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Last modified November 30 01:30 EST 2023. Contains 367452 sequences. (Running on oeis4.)