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List of numbers k such that k=6*r+1=m*q, m>=q and n>=g where number m is 6*n+1 or 6*n-1 and number q is 6*g+1 or 6*g-1.
5

%I #7 May 04 2024 09:23:48

%S 1,7,25,49,13,55,91,121,169,19,85,133,187,247,289,361,25,115,175,253,

%T 325,391,475,529,625,31,145,217,319,403,493,589,667,775,841,961,37,

%U 175,259,385,481,595,703,805,925,1015,1147,1225,1369,43,205,301,451,559,697

%N List of numbers k such that k=6*r+1=m*q, m>=q and n>=g where number m is 6*n+1 or 6*n-1 and number q is 6*g+1 or 6*g-1.

%C Triangle begins:

%C 1 (for row n=0)

%C 7 25 49 (for row n=1)

%C 13 55 91 121 169 (for row n=2)

%C 19 85 133 187 247 289 361 (for row n=3)

%C 25 115 175 253 325 391 475 529 625 (for row n=4)

%C 31 145 217 319 403 493 589 667 775 841 961 (for row n=5)

%e a(1)=1 because 1=6*0+1=1*1=(6*0+1)*(6*0+1);

%e a(2)=7 because 7=6*1+1=7*1=(6*1+1)*(6*0+1);

%e a(3)=25 because 25=6*4+1=5*5=(6*1-1)*(6*1-1);

%e a(4)=49 because 49=6*8+1=7*7=(6*1+1)*(6*1+1);

%e a(5)=13 because 13=13*1=(6*2+1)*(6*0+1);

%e a(6)=55 because 55=6*9+1=11*5=(6*2-1)*(6*1-1);

%e a(7)=91 because 91=13*7=(6*2+1)*(6*1+1);

%e a(8)=121 because 121=6*20+1=11*11=(6*2-1)*(6*2-1);

%e a(9)=169 because 169=6*28+1=13+13=(6*2+1)*(6*2+1);

%e a(10)=19 because 19=6*3+1=19*1=(6*3+1)*(6*0+1).

%Y Cf. A007310.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Feb 26 2010

%E Entries checked by _R. J. Mathar_, Apr 14 2010