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: Christina Steffan

Christina Steffan's wiki page.

Christina Steffan has authored 6 sequences.

A276478 Number of points in square lattice in and on the boundary of the area encompassed by two arcs of radius n and centers at (0,0) and (n,0).

Original entry on oeis.org

1, 2, 5, 12, 19, 34, 45, 56, 77, 98, 127, 148, 169, 206, 239, 280, 311, 350, 393, 440, 495, 534, 593, 644, 697, 770, 827, 896, 957, 1026, 1105, 1168, 1255, 1330, 1417, 1512, 1579, 1678, 1759, 1868, 1969, 2050, 2159, 2256, 2377, 2490, 2585, 2704, 2811, 2942
Offset: 0

Views

Author

Christina Steffan, Sep 05 2016

Keywords

Links

Crossrefs

Cf. A057961, A093731.

Programs

  • PARI
    a(n) = my(m = floor(n*sqrt(3)/2)); 1 - 3*n - 2*(n-1)*m + 4*sum(k=0, m, sqrtint(n^2-k^2)); \\ Michel Marcus, Mar 07 2021

Formula

a(n) = 1 - 3*n - 2*(n-1)*m(n) + 4 * Sum_{k=0..m(n)} floor(sqrt(n^2-k^2)) where m(n) = floor(n*sqrt(3)/2). - Franz Vrabec, Oct 02 2016
a(n)/n^2 tends to A093731 as n tends to infinity. - Rémy Sigrist, Mar 07 2021

Extensions

More terms from Franz Vrabec, Oct 02 2016

A268597 Smallest x such that x-1 mod phi(x) = n, or 0 if no such x exists.

Original entry on oeis.org

1, 4, 9, 8, 25, 18, 15, 16, 21, 50, 35, 36, 33, 98, 39, 32, 65, 54, 51, 100, 45, 70, 95, 72, 69, 338, 63, 196, 161, 110, 87, 64, 93, 130, 75, 108, 217, 182, 99, 200, 185, 170, 123, 140, 117, 190, 215, 144, 141, 250, 235
Offset: 0

Views

Author

Christina Steffan, Feb 08 2016

Keywords

Comments

Conjecture: a(n) > 0 for all n.

Crossrefs

Cf. A215486.

Programs

  • PARI
    a(n) = {my(x = 1); while ((x-1) % eulerphi(x) != n, x++); x;} \\ Michel Marcus, Feb 27 2016

A259728 Sum of digits of a(n) equals the sum of digits of 4*a(n).

Original entry on oeis.org

0, 3, 6, 9, 15, 18, 27, 30, 33, 36, 39, 45, 48, 51, 54, 57, 60, 63, 66, 69, 81, 84, 87, 90, 93, 96, 99, 105, 108, 126, 129, 135, 138, 150, 153, 156, 159, 165, 168, 177, 180, 183, 186, 189, 195, 198, 225, 228, 252, 261, 264, 267, 270, 273, 282, 291, 294, 297
Offset: 1

Views

Author

Christina Steffan, Jul 05 2015

Keywords

Comments

A007953(a(n)) = A007953(4*a(n)).
a(n) is a multiple of 3, but not all multiples of 3 belong to the sequence: e.g., 12 = 4*3: A007953(12) = 1 + 2 = 3, but A007953(4*12) = A007953(48) = 4 + 8 = 12.

Examples

			15 belongs to the sequence, because A007953(15) = 6 = A007953(60) = A007953(4*15).

Crossrefs

Cf. A007953, A070279, A259727, A259729.

Programs

  • Magma
    [n: n in [0..400] | &+Intseq(n) eq &+Intseq(4*n)]; // Vincenzo Librandi, Aug 05 2015

Extensions

More terms from Vincenzo Librandi, Aug 05 2015

A259729 Sum of digits of a(n) equals the sum of digits of 5*a(n).

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 126, 144, 162, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 297, 306, 324, 342, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 477, 495, 504, 522, 540, 549, 558, 567, 576, 585, 594
Offset: 1

Views

Author

Christina Steffan, Jul 05 2015

Keywords

Comments

A007953(a(n)) = A007953(5*a(n)).
a(n) is a multiple of 9, but not all multiples of 9 belong to the sequence: 117 = 13*9: A007953(117) = 1 + 1 + 7 = 9, but A007953(5*117) = A007953(585) = 5 + 8 + 5 = 18.

Examples

			18 belongs to the sequence, because A007953(18) = 9 = A007953(90) = A007953(5*18).

Crossrefs

Cf. A007953, A070279, A259727, A259728.

Programs

  • Magma
    [n: n in [0..800] | &+Intseq(n) eq &+Intseq(5*n)]; // Vincenzo Librandi, Aug 05 2015
  • Mathematica
    Select[Range[0, 600], Total@ IntegerDigits@ # == Total@ IntegerDigits[5 #] &] (* Michael De Vlieger, Aug 05 2015 *)

A259727 Sum of digits of a(n) equals the sum of digits of 3*a(n).

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 72, 81, 90, 99, 108, 117, 135, 144, 171, 180, 189, 198, 207, 234, 270, 279, 288, 297, 342, 351, 360, 396, 405, 414, 441, 450, 459, 486, 495, 504, 540, 549, 558, 576, 585, 594, 639, 648, 657, 693, 702, 711, 720, 729, 756, 765, 783, 792
Offset: 1

Views

Author

Christina Steffan, Jul 04 2015

Keywords

Comments

A007953(a(n)) = A007953(3*a(n)).
a(n) is a multiple of 9, but not all multiples of 9 belong to the sequence: e.g., 63 = 7*9: A007953(63) = 6 + 3 = 9, but A007953(3*63) = A007953(189) = 1 + 8 + 9 = 18.

Examples

			99 belongs to the sequence, because A007953(99) = 18 = A007953(297) = A007953(3*99).

Crossrefs

Cf. A007953, A070279, A259728, A259729.

Programs

  • Magma
    [n: n in [0..800] | &+Intseq(n) eq &+Intseq(3*n)]; // Vincenzo Librandi, Aug 05 2015
  • Mathematica
    Select[Range[0, 800], Total@ IntegerDigits@ # == Total@ IntegerDigits[3 #] &] (* Michael De Vlieger, Aug 05 2015 *)
  • PARI
    select(x->sumdigits(x)==sumdigits(3*x),vector(10^4,n,n)) \\ Joerg Arndt, Jul 04 2015

A145172 Number of pentagonal numbers needed to represent n with greedy algorithm.

Original entry on oeis.org

1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 2, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 2, 3, 4, 5, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 2, 3, 4, 5, 6, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 2, 3, 4, 5, 6, 3, 4, 5, 6
Offset: 1

Views

Author

Christina Steffan (christina.steffan(AT)gmx.at), Oct 03 2008

Keywords

Comments

Sequence is unbounded.

Examples

			a(21)=6 since 21 = 12+5+1+1+1+1.

Links

Crossrefs

Cf. A000326 (pentagonal numbers), A053610, A057945, A180447, A192988.

Programs

  • PARI
    a(n)={my(s=0); forstep(k=(sqrtint(24*n+1)+1)\6, 1, -1, my(t=k*(3*k-1)/2); s+=n\t; n%=t); s} \\ Andrew Howroyd, Apr 21 2021

Extensions

Terms a(41) and beyond from Andrew Howroyd, Apr 21 2021

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