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 A249558 a(a(n)) is a triangular number. 0
 1, 3, 6, 2, 7, 10, 15, 9, 21, 28, 12, 36, 14, 45, 55, 17, 66, 19, 78, 22, 91, 105, 24, 120, 26, 136, 29, 153, 171, 31, 190, 33, 210, 35, 231, 253, 38, 276, 40, 300, 42, 325, 44, 351, 378, 47, 406, 49, 435, 51, 465, 53, 496, 56, 528, 561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS To build T: always use the smallest integer not yet present in T and not leading to a contradiction. All triangular numbers appear in their natural order. Density of T: it appears that more than 50% of the terms are triangular. Arie Groeneveld computed a million terms in less than 1.5 seconds using the language J. REFERENCES Eric Angelini, Postings to Sequence Fans Mailing List, Mar 02 2011 and Mar 03 2011. LINKS EXAMPLE T = 1,... meaning that the first term of T is a triangular number (true) The next term can't be 2 as '2' would mean that the second term of T is a triangular term -- which is false, 2 is not a triangular number -- see A000217 Then: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3, We have to put a triangular number 't' in third position: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,t, Thus: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6, Thus: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,* * t Now we need to replace the first star with "the smallest integer not yet present in T and not leading to a contradiction": Thus: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,* t Next star is replaced by "the smallest etc." which can't be 4, 5 or 6 -- thus 7 (the 4th term of T is not a triangular number, the 5th neither -- as it would be '5' -- and '6' is already in T): Thus: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,t and: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,t  t We replace the next two 't' with two triangular numbers: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,10,15, and mark accordingly the 10th and 15th term of T with 't': n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,10,15,     t              t The next 'hole' we have to fill in T is the 8th; we put '9': n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,10,15,9,   t              t and we add accordingly a 't' in 9th position: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,10,15,9,t, t              t Now two more triangular numbers: n : 1 2 3 4 5 6  7  8 9  10 11 12 13 14 15 16 17 18 19 20 T = 1,3,6,2,7,10,15,9,21,28,            t ... etc. PROG (J) arr249558 =: monad define   n=. # (, 8+{:)^:(y>+/)^:_[ 6 15   ti=. (#~y>])+/\ 0 1 1 3 1 2, ; , &2 2&.>^:(])+/\ 3 1 3, ; , & 2 2&.>^:(^:(

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Last modified April 13 17:30 EDT 2021. Contains 342936 sequences. (Running on oeis4.)