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 A257175 The smallest m such that the m-th triangular number is greater than or equal to half the n-th triangular number. 1
 0, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 48, 49, 50, 51, 51, 52, 53, 53, 54, 55, 56, 56, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The a(n)-th triangular number is the smallest triangular number that is greater than or equal to half of the n-th triangular number. LINKS Matthew Scroggs, Table of n, a(n) for n = 0..10000 FORMULA a(n) = ceiling((sqrt(2n^2 + 2n + 1) - 1)/2). - Charles R Greathouse IV, Apr 17 2015 EXAMPLE For n=4, the 4th triangular number is 10. a(4)=3 as the 3rd triangular number is the first which is 5 or more. MATHEMATICA f[n_] := Block[{t = Accumulate[Range@ n], k, m}, {1}~Join~Rest@ Flatten@ Reap@ For[k = 1, k < n, m = 1; While[t[[m]] < t[[k]]/2, m++]; Sow[m], k++]]; f@ 80 (* Michael De Vlieger, Apr 17 2015 *) PROG (Python) def tri(n): ... return .5*n*(n+1) . for n in range(1, 10001): ... k = 1 ... while 2*tri(k)exact (/ (+ -1 (sqrt (+ (* 2 n n) n n 1))) 2))) ;; After Greathouse's formula - Antti Karttunen, Apr 18 2015 CROSSREFS Cf. A000217. Sequence in context: A057561 A064726 A274616 * A210357 A057359 A076538 Adjacent sequences:  A257172 A257173 A257174 * A257176 A257177 A257178 KEYWORD nonn,easy AUTHOR Matthew Scroggs, Apr 17 2015 STATUS approved

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)