A263729 -id:A263729 - cp's OEIS frontend

A263730 Irregular triangle read by rows in which row n > 1 lists k such that (k^2 + k*n)/(k + 1) is an integer.

0, 0, 1, 0, 2, 0, 1, 3, 0, 4, 0, 1, 2, 5, 0, 6, 0, 1, 3, 7, 0, 2, 8, 0, 1, 4, 9, 0, 10, 0, 1, 2, 3, 5, 11, 0, 12, 0, 1, 6, 13, 0, 2, 4, 14, 0, 1, 3, 7, 15, 0, 16, 0, 1, 2, 5, 8, 17, 0, 18, 0, 1, 3, 4, 9, 19, 0, 2, 6, 20, 0, 1, 10, 21, 0, 22, 0, 1, 2, 3, 5, 7, 11, 23, 0, 4, 24, 0, 1, 12, 25

Offset: 2

Juri-Stepan Gerasimov, Oct 25 2015

Minimal value of k is 0 and maximal value of k is n - 2 for n-th row.
Length of rows gives A000005.
Sum of rows gives A065608.

			  n\k| 0   1   2   3   4   5   6   7   8   9  10
  ---+------------------------------------------
   0 | 0
   1 | 0   1   2   3   4   5   6   7   8   9  10
   2 | 0
   3 | 0   1
   4 | 0   2
   5 | 0   1   3
   6 | 0   4
   7 | 0   1   2   5
   8 | 0   6
   9 | 0   1   3   7
  10 | 0   2   8
  11 | 0   1   4   9
  12 | 0  10
  13 | 0   1   2   3   5  11

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Cf. A000005, A065608, A027750, A263729.

Table[Select[Range[0,n-2],Divisible[#^2+n #,#+1]&],{n,30}]//Flatten (* Harvey P. Dale, Dec 27 2016 *)

tabf(nn) = {for (n=2, nn, for (k=0, n, if (!((k^2 + k*n) % (k+1)), print1(k, ", "));); print(););} \\ Michel Marcus, Oct 25 2015

a(n) = A027750(n) - 1.

A263770 Smallest prime q such that (prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer.

Original entry on oeis.org

7, 5, 7, 17, 13, 29, 19, 41, 73, 31, 97, 191, 43, 89, 97, 109, 61, 311, 137, 73, 149, 241, 337, 181, 197, 103, 313, 109, 331, 229, 257, 397, 139, 281, 151, 457, 317, 821, 337, 349, 181, 547, 193, 389, 199, 401, 1061, 449, 229, 461, 937, 241, 727, 757, 1033, 1321, 271, 1361, 557

Offset: 1

Juri-Stepan Gerasimov, Oct 25 2015

nonn

Least prime q such that q == 1 (mod prime(n) + 1).

Consists of the initial terms of sequences A002476, A002144, A002476, A007519, A068228, A140444, A061237, A141881, A107008, A132230, A133870, A141868, A124826, A142292, A142398, A141948, A088955, A142003, ...

Cf. A263729, A263730, A263769.

Table[q = 2; While[! IntegerQ[(Prime[n]^2 + q Prime@ n)/(Prime@ n + 1)], q = NextPrime@ q]; q, {n, 59}] (* Michael De Vlieger, Oct 26 2015 *)

a(n) = {p = prime(n); q = 2; while ((p^2 + p*q) % (p + 1), q = nextprime(q+1)); q;} \\ Michel Marcus, Oct 26 2015

5 is in this sequence because (prime(2)^2 + 5*prime(2))/(prime(2) + 1) = 6 and 5 is prime.

cp's OEIS Frontend

A263730 Irregular triangle read by rows in which row n > 1 lists k such that (k^2 + k*n)/(k + 1) is an integer.

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