

A053726


"Flag numbers": number of dots that can be arranged in successive rows of K, K1, K, K1, K, ..., K1, 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
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OFFSET

1,1


COMMENTS

Numbers of the form F(K, L) = KL+(K1)(L1), 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 2n1, 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
Also area of (over 45 degree) rotated rectangles with sides > 1. The area of such rectangles is 2ab  a  b + 1 = 1/2((2a1)(2b1)+1).
Example: Here a = 3 and b = 5. The area = 23.
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LINKS



FORMULA

a(n) = n + A000720(A071904(n)). [The above formula reduces to this. A000720(k) gives number of primes <= k, and A071904 gives the nth odd composite number.]
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PROG

(Scheme, with Antti Karttunen's IntSeqlibrary, two alternatives)
(define A053726 (MATCHINGPOS 1 1 (lambda (n) (and (> n 1) (not (prime? (+ n n 1)))))))
(Python)
from sympy import isprime
def ok(n): return n > 1 and not isprime(2*n1)


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).
Differs from its subsequence A246371 for the first time at a(8) = 20, which is missing from A246371.


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



