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 A130335 Smallest k > 0 such that gcd(n*(n+1)/2, (n+k)*(n+k+1)/2) = 1. 4
 1, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 13, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 7, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 13, 2, 2, 10, 2, 2, 4, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 22, 2, 2, 7, 2, 2, 16, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First occurrence of 3k+1, k=0.. or 0 if unknown, limit = 2^31: 1, 6, 3, 12, 24, 90, 231, 84, 792, 0, 195, 3432, 780, 0, 3255, 6075, 73644, 51482970, 0, 924, 183540, 0, 45219, 0, 509124, 3842375445, 29259, 71484, 0, 0, 0, 2311539, 238547880, 0, 55380135, 893907420, 23303784, 0, 0, 208260975, 0, 0, 1744264599, 0, 0, 0, 1487657079, 665710275, 0, 0, 1963994955, 0, 319589424, 0, 0, 0, 4181294964, 0, 0, 383229924, ..., . - Robert G. Wilson v, Jun 03 2007 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Min{k>0: A050873(A000217(n+k),A000217(n))=1); a(n) = A130334(n) - n; a(n) > 1 for n>1; a(n) > 2 iff n mod 3 = 0: a(A001651(n))=2, a(A008585(n)) > 2 for n > 1. a(n) == 1 (mod 3) if a(n) != 2. - Robert G. Wilson v, Jun 03 2007 MATHEMATICA f[n_] := Block[{k = If[ n == 1 || Mod[n, 3] == 0, 1, 2]}, While[ GCD[n(n + 1)/2, (n + k)(n + k + 1)/2] != 1, k += 3 ]; k]; Array[f, 100] (* Robert G. Wilson v, Jun 03 2007 *) PROG (Python) from math import gcd def A130335(n): k, Tn, Tm = 1, n*(n+1)//2, (n+1)*(n+2)//2 while gcd(Tn, Tm) != 1: k += 1 Tm += k+n return k # Chai Wah Wu, Sep 16 2021 (PARI) a(n) = my(k=1); while (gcd(n*(n+1)/2, (n+k)*(n+k+1)/2) != 1, k++); k; CROSSREFS Cf. A000217, A050873. Cf. A001651, A008585. Cf. A130334. See A130336 and A130337 for record values and where they occur. Sequence in context: A082072 A082066 A179931 * A347236 A073246 A021790 Adjacent sequences: A130332 A130333 A130334 * A130336 A130337 A130338 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 28 2007 STATUS approved

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Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)