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.

User: Slav E. Angelov

Slav E. Angelov's wiki page.

Slav E. Angelov has authored 2 sequences.

A342711 Partial sums of A000267.

Original entry on oeis.org

1, 3, 6, 9, 13, 17, 22, 27, 32, 38, 44, 50, 57, 64, 71, 78, 86, 94, 102, 110, 119, 128, 137, 146, 155, 165, 175, 185, 195, 205, 216, 227, 238, 249, 260, 271, 283, 295, 307, 319, 331, 343, 356, 369, 382, 395, 408, 421, 434, 448, 462, 476, 490, 504, 518, 532, 547
Offset: 0

Views

Author

Slav E. Angelov, Mar 19 2021

Keywords

Comments

a(n) = A109512(n+1) for n = 0..23.
This sequence is the partial sums of A000267, which in turn is the partial sums of A240025.
It can be used to obtain a formula for the n-th term of A342712.

Crossrefs

Cf. A000267, A240025, A342712.

Programs

  • Mathematica
    Accumulate @ Array[Floor @ Sqrt[4*# + 1] &, 100, 0] (* Amiram Eldar, Mar 19 2021 *)
  • PARI
    a(n) = sum(i=0, n, sqrtint(4*i+1)); \\ Michel Marcus, Mar 19 2021

A342712 Partial sums of A248333.

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 6, 9, 13, 17, 22, 28, 34, 41, 49, 58, 67, 77, 88, 100, 112, 125, 139, 154, 170, 186, 203, 221, 240, 260, 280, 301, 323, 346, 370, 395, 420, 446, 473, 501, 530, 560, 590, 621, 653, 686, 720, 755, 791, 827, 864, 902, 941, 981, 1022, 1064, 1106
Offset: 1

Views

Author

Slav E. Angelov, Mar 20 2021

Keywords

Crossrefs

Cf. A248333, A000217, A342711.

Programs

  • PARI
    f(n) = sum(i=1, n, !(issquare(i-1) || issquare(floor(i-sqrt(i-1))))); \\ A248333
a(n) = sum(k=0, n, f(k)); \\ Michel Marcus, Mar 20 2021

Formula

a(n) = A000217(n) - A342711(n-1) for n >= 1. [Corrected by Georg Fischer, Dec 13 2022]

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