A130335 -id:A130335 - cp's OEIS frontend

A130336 Record values in A130335.

1, 2, 7, 10, 13, 22, 31, 37, 58, 79, 82, 94, 109, 118, 157, 178, 193, 214

Offset: 1

Reinhard Zumkeller, May 28 2007

f[n_] := Block[{k = 1}, While[ GCD[n(n + 1)/2, (n + k)(n + k + 1)/2] != 1, k++ ]; k]; t = Table[0, {1000}]; Do[a = f@n; If[a < 1001 && t[[a]] == 0, t[[a]] = n; Print[{a, n}], If[a > 1000, Print[{"Over 1000", n}]]], {n, 2^31 - 1}] (* Robert G. Wilson v, Jun 03 2007 *)

a(n) = A130335(A130337(n)).

A130335(k) < a(n) for k < A130337(n).

a(13)-a(16) from Robert G. Wilson v, Jun 03 2007
Added a(17) and corrected a(12) by Chai Wah Wu, Sep 16 2021
a(18) from Chai Wah Wu, Sep 23 2021

A130337 Where record values occur in A130335.

Original entry on oeis.org

1, 2, 3, 12, 24, 84, 195, 780, 924, 29259, 71484, 2311539, 23303784, 208260975, 319589424, 383229924, 11962377504, 178523171904

Offset: 1

Reinhard Zumkeller, May 28 2007

Cf. A130335, A130336.

f[n_] := Block[{k = 1}, While[ GCD[n(n + 1)/2, (n + k)(n + k + 1)/2] != 1, k++ ]; k]; t = Table[0, {1000}]; Do[a = f@n; If[a < 1001 && t[[a]] == 0, t[[a]] = n; Print[{a, n}], If[a > 1000, Print[{"Over 1000", n}]]], {n, 2^31 - 1}] (* Robert G. Wilson v, Jun 03 2007 *)

A130336(n) = A130335(a(n)).

A130335(k) < A130336(n) for k

a(13)-a(16) from Robert G. Wilson v, Jun 03 2007
a(17) from Chai Wah Wu, Sep 16 2021
a(18) from Chai Wah Wu, Sep 23 2021

A130334 Smallest m>n such that the m-th and n-th triangular numbers are coprime.

Original entry on oeis.org

2, 4, 10, 6, 7, 10, 9, 10, 13, 12, 13, 22, 15, 16, 22, 18, 19, 22, 21, 22, 25, 24, 25, 37, 27, 28, 37, 30, 31, 37, 33, 34, 37, 36, 37, 46, 39, 40, 46, 42, 43, 46, 45, 46, 52, 48, 49, 58, 51, 52, 58, 54, 55, 58, 57, 58, 61, 60, 61, 73, 63, 64, 73, 66, 67, 70, 69, 70, 73, 72, 73

Offset: 1

Reinhard Zumkeller, May 28 2007

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Triangular Number
Eric Weisstein's World of Mathematics, Relatively Prime

Cf. A000217, A026741, A109007, A130335.

from math import gcd
def A130334(n):
    k, Tn, Tm = n+1, n*(n+1)//2, (n+1)*(n+2)//2
    while gcd(Tn,Tm) != 1:
        k += 1
        Tm += k
    return k # Chai Wah Wu, Sep 16 2021

a(n) > n+1 for n>1; a(n) > n+2 for n with n mod 3 = 0;

a(n) = n + A130335(n).

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A130336 Record values in A130335.

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A130337 Where record values occur in A130335.

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A130334 Smallest m>n such that the m-th and n-th triangular numbers are coprime.

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