A173865 -id:A173865 - cp's OEIS frontend

A174052 The sum of the numbers in n-th row of alternant triangle A173865.

Original entry on oeis.org

1, 40, 81, 296, 449, 984, 1301, 2320, 2913, 4558, 5441

Offset: 1

Juri-Stepan Gerasimov, Mar 06 2010

nonn

Cf. A007310, A140475, A173825, A173865.

A174027 Alternating triangle (version 2) read by rows: composites k such that k=6m-+1=rj r>=j and n>=q>0 where r=6n-1 or r=6n+1 and j=6q-1 or j=6q+1.

Original entry on oeis.org

35, 25, 49, 65, 77, 143, 55, 91, 121, 169, 95, 119, 209, 221, 323, 65, 133, 187, 247, 289, 361, 125, 161, 275, 299, 425, 437, 575, 115, 175, 253, 325, 391, 475, 529, 625, 155, 203, 341, 377, 527, 589, 713, 725, 899, 145, 217, 319, 403, 493, 569, 667, 775, 841

Offset: 1

Juri-Stepan Gerasimov, Mar 06 2010, Mar 17 2010

Composites of form 6*m-1 are in even (0,2,4,..) rows of alternating triangle only. Composites of form 6*m+1 are in odd (1,3,5,..) rows of alternating triangle only. 1 UNION nontrivial primes UNION A174027(without repetition) = A140475 U A174027(without repetition) = A007310 = numbers of form 6*n+-1, where alternating triangle (version 1) is A173865.

			Triangle begins:
35(=7*5) in even 0th row;
25(=5*5) and 49(=7*7) in odd 1st row;
65(=13*5), 77(=11*7) and 143(=13*11) in even 2nd row.

Cf. A007310, A140475, A173825, A173865.

A174130 List of numbers k such that k=6r-1=mq, m>=q and n>=g where m=6n-1 or m=6n+1 and q=6g-1 or 6g+1.

Original entry on oeis.org

5, 35, 11, 65, 77, 143, 17, 95, 119, 209, 221, 323, 23, 125, 161, 275, 299, 425, 437, 575, 29, 155, 217, 341, 377, 527, 551, 713, 725, 999, 35, 185, 245, 407, 455, 529, 565, 851, 875, 1073, 1085, 1295, 41, 215, 287, 473, 533, 731, 779, 943, 1075, 1189

Offset: 1

Juri-Stepan Gerasimov, Mar 09 2010

nonn

Alternating triangle A173865 read by odd rows. A173825 U A174130 = A173865.

			a(1)=5 because 5=6*1-1=(6*1-1)*(6*0+1); a(2)=35 because 35=6*6-1=(6*1-1)*(6*1+1); a(3)=11 because 11=6*2-1=(6*2-1)*(6*0+1).

Cf. A173825, A173865.

A174358 Alternating triangle (version 3) read by rows: numbers k such that k=6m+3-+2=rj , r>=j and n>=q where r=6n+3-2 or r=6n+3+2 and j=6q+3-2 or j=6q+3+2.

Original entry on oeis.org

5, 1, 25, 11, 35, 77, 7, 55, 49, 121, 17, 65, 119, 143, 221, 13, 85, 91, 181, 109, 289, 23, 95, 161, 209, 299, 323, 437, 19, 115, 133, 253, 247, 391, 361, 529, 29, 125, 203, 275, 377, 425, 551, 575, 725, 25, 145, 175, 319, 325, 493, 475, 667, 625, 841, 35, 185, 245

Offset: 1

Juri-Stepan Gerasimov, Mar 17 2010, Mar 30 2010

Numbers of form 6*m+3+2 are in even rows, numbers of form 6*m+3-2 are in odd rows. Numbers of alternating triangle (version 1) are A173865. Numbers of alternating triangle (version 2) are A174027.

			Triangle begins: 5*1 1*1 5*5 11*1 7*5 11*7 7*1 11*5 7*7 11*11 17*1 13*5 17*7 13*11 17*13 13*1 17*5 13*7 17*11 13*13 17*17.. or 5(in even 0 row) 1 25(in odd 1 row) 11 35 77(in even 2 row) 7 55 49 121(in odd 3 row) 17 65 119 143 221(in even 4 row) 13 85 91 181 169 289(in odd 5 row)..
That is:
5;
1, 25;
11, 35, 77;
7, 55, 49, 121;
17, 65, 119, 143;

Cf. A007310, A173825, A173865, A174027.

cp's OEIS Frontend

A174052 The sum of the numbers in n-th row of alternant triangle A173865.

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A174027 Alternating triangle (version 2) read by rows: composites k such that k=6m-+1=rj r>=j and n>=q>0 where r=6n-1 or r=6n+1 and j=6q-1 or j=6q+1.

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A174130 List of numbers k such that k=6r-1=mq, m>=q and n>=g where m=6n-1 or m=6n+1 and q=6g-1 or 6g+1.

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A174358 Alternating triangle (version 3) read by rows: numbers k such that k=6m+3-+2=rj , r>=j and n>=q where r=6n+3-2 or r=6n+3+2 and j=6q+3-2 or j=6q+3+2.

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cp's OEIS Frontend

A174052 The sum of the numbers in n-th row of alternant triangle A173865.

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Author

Keywords

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A174027 Alternating triangle (version 2) read by rows: composites k such that k=6*m-+1=r*j r>=j and n>=q>0 where r=6*n-1 or r=6*n+1 and j=6*q-1 or j=6*q+1.

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A174130 List of numbers k such that k=6*r-1=m*q, m>=q and n>=g where m=6*n-1 or m=6*n+1 and q=6*g-1 or 6*g+1.

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A174358 Alternating triangle (version 3) read by rows: numbers k such that k=6*m+3-+2=r*j , r>=j and n>=q where r=6*n+3-2 or r=6*n+3+2 and j=6*q+3-2 or j=6*q+3+2.

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A174027 Alternating triangle (version 2) read by rows: composites k such that k=6m-+1=rj r>=j and n>=q>0 where r=6n-1 or r=6n+1 and j=6q-1 or j=6q+1.

A174130 List of numbers k such that k=6r-1=mq, m>=q and n>=g where m=6n-1 or m=6n+1 and q=6g-1 or 6g+1.

A174358 Alternating triangle (version 3) read by rows: numbers k such that k=6m+3-+2=rj , r>=j and n>=q where r=6n+3-2 or r=6n+3+2 and j=6q+3-2 or j=6q+3+2.