proposed

approved

editing

proposed

allocated for Martin RennerIrregular triangle T(n,k) read by rows with 1 <= k <= A091887 even indices 2i such that n-th irregular prime p (A000928) divides the numerator of the Bernoulli numbers B_{2i} (A000367) with 0 <= 2i <= p-3.

32, 44, 58, 68, 24, 22, 130, 62, 110, 84, 164, 100, 84, 20, 156, 88, 292, 280, 186, 300, 100, 174, 200, 382, 126, 240, 366, 196, 130, 94, 194, 292, 336, 338, 400, 86, 270, 486, 222, 52, 90, 92, 22, 592, 522, 20, 174, 338, 428, 80, 226, 236, 242, 554, 48, 224, 408, 502, 628, 32, 12, 200, 378, 290, 514, 260, 732, 220, 330, 628, 544, 744, 102, 66, 868, 162, 418, 520, 820, 156, 166

1,1

First index T(n,1) in row n is A035112(n).

Triangle starts with

n = 1 => p = 37 divides the numerator of B_{32} = -7709321041217;

n = 2 => p = 59: B_{44};

n = 3 => p = 67: B_{58};

n = 4 => p = 101: B_{68};

n = 5 => p = 103: B_{24};

n = 6 => p = 131: B_{22};

n = 7 => p = 149: B_{130};

n = 8 => p = 157: B_{62}, B_{110};

n = 9 => p = 233: B_{84};

etc.

T:=[]:

for j from 2 to 168 do

p:=ithprime(j);

B:=[]:

for i from 1 to (p-3)/2 do

if type(numer(bernoulli(2*i))/p, integer) then B:=[op(B), 2*i]: fi:

od:

T:=[op(T), op(B)];

od:

op(T);

Cf. A000367, A000928, A035112, A060974, A060975, A073276, A073277, A091887.

allocated

nonn,tabf

Martin Renner, Jun 23 2019

approved

editing

allocated for Martin Renner

recycled

allocated

recycled

approved