cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A135284 Sum of staircase twin primes according to the rule: top + bottom - next top.

Original entry on oeis.org

3, 1, 7, 7, 19, 25, 49, 43, 97, 79, 127, 121, 169, 187, 169, 217, 211, 259, 253, 277, 277, 409, 403, 403, 475, 541, 583, 595, 625, 511, 799, 817, 799, 835, 745, 1009, 1015, 1039, 1033, 1033, 1075, 1183, 1267, 1279, 1285, 1213, 1405, 1423, 1477, 1369, 1597, 1573
Offset: 1

Views

Author

Cino Hilliard, Dec 03 2007

Keywords

Comments

The case for bottom - top + next top produces A006512(n+1), the upper twin primes > 5.

Programs

  • PARI
    g(n) = for(x=1,n,y=twinu(x) + twinl(x) - twinl(x+1);print1(y",")) twinl(n) = / *The n-th lower twin prime. */ { local(c,x); c=0; x=1; while(c

Formula

We list the twin primes in staircase fashion as in A135283. Then a(n) = tl(n) + tu(n) + (-tl(n+1)).
a(n) = A054735(n)-A001359(n+1). - R. J. Mathar, Sep 10 2016

A135285 Sum of staircase twin primes according to the rule: top * bottom - next top.

Original entry on oeis.org

10, 24, 126, 294, 858, 1704, 3528, 5082, 10296, 11526, 18894, 22320, 32208, 36666, 38976, 51744, 57330, 72618, 79212, 96996, 120684, 175968, 186162, 212922, 271914, 324300, 359382, 381282, 411504, 434790, 655278, 674856, 684726, 735282, 776904
Offset: 1

Views

Author

Cino Hilliard, Dec 03 2007

Keywords

Comments

While there is multiplication and subtraction in the generation of this sequence, it is still called a sum because the arithmetic processes -,*,/ are derived from addition.

Programs

  • PARI
    g(n) = for(x=1,n,y=twinu(x) * twinl(x) - twinl(x+1);print1(y",")) twinl(n) = / *The n-th lower twin prime. */ { local(c,x); c=0; x=1; while(c

Formula

We list the twin primes in staircase fashion as in A135283. Then a(n) = tl(n) * tu(n) + (-tl(n+1)).
a(n) = A037074(n) -A001359(n+1). - R. J. Mathar, Sep 10 2016

A135286 Sum of staircase twin primes according to the rule: top * bottom + next top.

Original entry on oeis.org

20, 46, 160, 352, 940, 1822, 3670, 5284, 10510, 11800, 19192, 22678, 32590, 37060, 39430, 52222, 57868, 73180, 79834, 97690, 121522, 176830, 187084, 213964, 273052, 325498, 360616, 382564, 412822, 436408, 656920, 676510, 686440, 737044, 778942, 1041430, 1066072, 1103560, 1128934, 1193614, 1328332, 1514176, 1634572, 1665400, 1696522, 1743826, 2040634, 2109784, 2197810, 2215750
Offset: 1

Views

Author

Cino Hilliard, Dec 03 2007

Keywords

Comments

While there is multiplication in the generation of this sequence, it is still called a sum because the arithmetic processes -,*,/ are derived from addition.

Programs

  • PARI
    g(n) = for(x=1,n,y=twinu(x) * twinl(x) + twinl(x+1);print1(y",")) twinl(n) = / *The n-th lower twin prime. */ { local(c,x); c=0; x=1; while(c

Formula

We list the twin primes in staircase fashion as in A135283. Then a(n) = tl(n) * tu(n) + tl(n+1).
a(n) = A037074(n)+A001359(n+1). - R. J. Mathar, Sep 10 2016

Extensions

All the entries were wrong. They have been corrected by Franklin T. Adams-Watters, Apr 29 2008
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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