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A300288 Irregular triangle read by rows: row n contains numbers k such that -n<=k<=n and gcd(k, 2*n+1) != 1. 1
0, 0, 0, -3, 0, 3, 0, 0, -6, -5, -3, 0, 3, 5, 6, 0, 0, -9, -7, -6, -3, 0, 3, 6, 7, 9, 0, -10, -5, 0, 5, 10, -12, -9, -6, -3, 0, 3, 6, 9, 12, 0, 0, -15, -12, -11, -9, -6, -3, 0, 3, 6, 9, 11, 12, 15, -15, -14, -10, -7, -5, 0, 5, 7, 10, 14, 15, 0, -18, -15, -13, -12, -9, -6, -3, 0, 3, 6, 9, 12, 13, 15, 18, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row n contains 2*n+1 - phi(2*n+1) = A053193(n) terms. Row n has just one term (namely 0) if 2*n+1 is prime.

LINKS

Table of n, a(n) for n=1..84.

FORMULA

T(n,k) = A299714(n,k) - n.

EXAMPLE

Triangle starts:

[01]: 0,

[02]: 0,

[03]: 0,

[04]: -3, 0, 3,

[05]: 0,

[06]: 0,

[07]: -6, -5, -3, 0, 3, 5, 6,

[08]: 0,

[09]: 0,

[10]: -9, -7, -6, -3, 0, 3, 6, 7, 9,

[11]: 0,

[12]: -10, -5, 0, 5, 10,

[13]: -12, -9, -6, -3, 0, 3, 6, 9, 12,

[14]: 0,

[15]: 0,

[16]: -15, -12, -11, -9, -6, -3, 0, 3, 6, 9, 11, 12, 15,

[17]: -15, -14, -10, -7, -5, 0, 5, 7, 10, 14, 15,

[18]: 0,

[19]: -18, -15, -13, -12, -9, -6, -3, 0, 3, 6, 9, 12, 13, 15, 18,

[20]: 0,

...

PROG

(PARI) is(n, k)= ( gcd(k, 2*n+1)!=1 );

for (n=1, 33, for (k=-n, +n, if (is(n, k), print1(k, ", ") ); ); );

CROSSREFS

Cf. A299714.

Sequence in context: A247704 A127802 A165951 * A340555 A094901 A030220

Adjacent sequences: A300285 A300286 A300287 * A300289 A300290 A300291

KEYWORD

sign,tabf

AUTHOR

Joerg Arndt, Mar 02 2018

STATUS

approved

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Last modified February 4 19:22 EST 2023. Contains 360059 sequences. (Running on oeis4.)