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: Kritsada Moomuang

Kritsada Moomuang's wiki page.

Kritsada Moomuang has authored 37 sequences. Here are the ten most recent ones:

A383659 Decimal expansion of phi + 2*log(phi), where phi is the golden ratio.

Original entry on oeis.org

2, 5, 8, 0, 4, 5, 7, 6, 3, 8, 8, 6, 9, 1, 0, 1, 7, 4, 3, 2, 0, 0, 1, 0, 4, 6, 6, 1, 2, 1, 4, 3, 7, 4, 9, 6, 3, 9, 9, 0, 6, 7, 7, 8, 4, 8, 5, 7, 7, 0, 8, 3, 9, 0, 1, 4, 5, 7, 4, 8, 4, 9, 6, 0, 3, 8, 5, 5, 8, 8, 1, 9, 8, 0, 3, 5, 3, 4, 5, 9, 9, 8, 5, 3, 1, 2, 2
Offset: 1

Views

Author

Kritsada Moomuang, Jun 11 2025

Keywords

Examples

			2.58045763886910174320...

Crossrefs

Cf. A001622, A002390, A202543, A384238, A384682.

Programs

  • Mathematica
    RealDigits[GoldenRatio + 2 * Log[GoldenRatio], 10, 100, 0][[1]]

Formula

Equals Integral_{x=0..1} sqrt(1/x + sqrt(1/x + sqrt(1/x + ...))) dx.
Equals Integral_{x=0..1} (1 + sqrt(1 + 4/x))/2 dx.
Equals A001622 + A202543.

A384932 Decimal expansion of tan(1) + sec(1).

Original entry on oeis.org

3, 4, 0, 8, 2, 2, 3, 4, 4, 2, 3, 3, 5, 8, 2, 7, 8, 4, 8, 4, 1, 8, 7, 2, 8, 0, 4, 8, 8, 5, 7, 0, 1, 0, 3, 6, 6, 5, 5, 7, 6, 4, 7, 4, 2, 7, 4, 7, 5, 5, 2, 9, 3, 3, 7, 2, 1, 9, 1, 0, 4, 8, 8, 3, 5, 5, 7, 6, 7, 6, 8, 0, 8, 4, 1, 3, 3, 2, 3, 9, 9, 5, 4, 7, 6, 9, 4
Offset: 1

Views

Author

Kritsada Moomuang, Jun 12 2025

Keywords

Comments

The continued fraction expansion of this constant - 1 is A133265.

Examples

			3.408223442335827848481...

Crossrefs

Cf. A049471, A073448, A133265, A248617.

Programs

  • Mathematica
    RealDigits[Tan[1] + Sec[1], 10, 100, 0][[1]]
  • PARI
    tan(1) + 1/cos(1) \\ Amiram Eldar, Jun 13 2025

Formula

Equals A049471 + A073448.
Equals 4 + Integral_{x=0..1} sin(x)/(sin(x) - 1) dx.
Equals exp(Integral_{x=0..1} sec(x) dx).
Equals exp(A248617). - Hugo Pfoertner, Jun 13 2025

A384682 Decimal expansion of (5/6)*phi = 5*(1 + sqrt(5))/12, where phi is the golden ratio.

Original entry on oeis.org

1, 3, 4, 8, 3, 6, 1, 6, 5, 7, 2, 9, 1, 5, 7, 9, 0, 4, 0, 1, 7, 0, 4, 8, 9, 0, 2, 8, 6, 3, 8, 0, 3, 1, 7, 6, 4, 7, 6, 6, 9, 2, 4, 3, 1, 6, 5, 0, 4, 8, 0, 2, 3, 8, 5, 1, 1, 2, 8, 7, 3, 8, 5, 2, 2, 5, 4, 3, 8, 3, 7, 1, 9, 0, 1, 5, 7, 5, 2, 0, 4, 1, 4, 2, 2, 6, 7
Offset: 1

Views

Author

Kritsada Moomuang, Jun 06 2025

Keywords

Examples

			1.34836165729157904017...

Crossrefs

Cf. A001622, A021016, A134944, A134946, A384238.

Programs

  • Mathematica
    RealDigits[GoldenRatio * 5/6, 10, 100, 0][[1]]

Formula

Minimal polynomial: 36*x^2 - 30*x - 25.
Equals Integral_{x=0..1} sqrt(x + sqrt(x + sqrt(x + ...))) dx.
Equals Integral_{x=0..1} (1 + sqrt(1 + 4*x))/2 dx.
Equals 10*A134944/3 = 5*A134946. - Hugo Pfoertner, Jun 07 2025

A384238 Decimal expansion of sqrt(5) - log(phi) - 1, where phi is the golden ratio.

Original entry on oeis.org

7, 5, 4, 8, 5, 6, 1, 5, 2, 4, 4, 0, 1, 8, 6, 2, 4, 8, 9, 1, 1, 4, 1, 4, 7, 5, 5, 3, 0, 6, 9, 0, 7, 8, 1, 2, 3, 0, 5, 4, 3, 4, 0, 2, 5, 2, 2, 5, 8, 6, 5, 2, 0, 4, 6, 0, 9, 8, 7, 9, 0, 7, 6, 5, 7, 0, 3, 5, 7, 0, 5, 8, 0, 2, 9, 5, 8, 3, 1, 2, 5, 0, 0, 2, 4, 0, 4
Offset: 0

Views

Author

Kritsada Moomuang, May 22 2025

Keywords

Examples

			0.75485615244018624891...

Crossrefs

Cf. A002163, A002390, A384682

Programs

  • Mathematica
    RealDigits[Sqrt[5] - Log[GoldenRatio] - 1, 10, 100, -1][[1]]

Formula

Equals Integral_{x=0..1} 2/(1 + sqrt(1 + 4*x)) dx.
Equals Integral_{x=0..1} 1/(1 + x/(1 + x/(1 + x/...))) dx.
Equals A002163 - A002390 - 1.

A384059 Decimal expansion of the circumradius of a regular pentagonal prism of edge length 1.

Original entry on oeis.org

9, 8, 6, 7, 1, 5, 1, 5, 5, 3, 2, 5, 9, 8, 3, 1, 0, 7, 3, 2, 0, 7, 0, 0, 0, 5, 5, 8, 4, 0, 6, 6, 8, 9, 1, 7, 8, 7, 2, 8, 5, 0, 4, 5, 2, 2, 3, 2, 0, 3, 5, 0, 7, 3, 7, 8, 6, 4, 3, 1, 5, 5, 2, 4, 8, 6, 1, 9, 6, 1, 0, 4, 0, 5, 4, 5, 3, 8, 1, 0, 3, 3, 0, 5, 7, 9, 1
Offset: 0

Views

Author

Kritsada Moomuang, May 18 2025

Keywords

Examples

			0.98671515532598310...

Crossrefs

Cf. A102771 (volume), A300074 (midradius), A384036 (surface area).

Programs

  • Mathematica
    RealDigits[1/2 * Sqrt(3 + 2/Sqrt(5)), 10, 100, -1][[1]]

Formula

Equals (1/2)*sqrt(3 + 2/sqrt(5)).
Minimal polynomial: 80*x^4 - 120*x^2 + 41. - Stefano Spezia, May 18 2025

A384036 Decimal expansion of the surface area of a regular pentagonal prism of edge length 1.

Original entry on oeis.org

8, 4, 4, 0, 9, 5, 4, 8, 0, 1, 1, 7, 7, 9, 3, 3, 8, 4, 5, 5, 1, 8, 0, 2, 3, 9, 5, 4, 7, 7, 7, 2, 1, 9, 1, 9, 8, 8, 1, 4, 7, 4, 8, 3, 4, 0, 0, 2, 0, 3, 9, 6, 6, 5, 8, 4, 1, 4, 1, 8, 9, 4, 1, 4, 0, 4, 7, 7, 3, 7, 9, 8, 4, 4, 1, 7, 9, 3, 2, 4, 6, 2, 6, 6, 4, 8, 8
Offset: 1

Views

Author

Kritsada Moomuang, May 17 2025

Keywords

Examples

			8.4409548011779338455...

Crossrefs

Cf. A178809.
Cf. A102771 (volume), A300074 (midradius), A384059 (circumradius).

Programs

  • Mathematica
    RealDigits[5 + 1/2 * Sqrt(25 + 10 * Sqrt(5)), 10, 100, 0][[1]]

Formula

Equals 5 + (1/2)*sqrt(25 + 10*sqrt(5)).
Minimal polynomial: 16*x^4 - 320*x^3 + 2200*x^2 - 6000*x + 5125. - Stefano Spezia, May 17 2025

A383692 a(n) = round(Chi(n)) where Chi(x) is the cosh integral function.

Original entry on oeis.org

1, 2, 5, 10, 20, 43, 96, 220, 519, 1246, 3036, 7480, 18599, 46596, 117478, 297780, 758319, 1938952, 4975454, 12807826, 33063593, 85572336, 221983185, 577057696, 1502975453, 3921470496, 10248248560, 26822559296, 70299597879, 184486604704, 484727787984
Offset: 1

Views

Author

Kritsada Moomuang, May 05 2025

Keywords

Comments

This sequence is almost the same as A383542, except at n = 0, where Chi(0) is undefined, and at n = 2, where Shi(2) = 2.50156... rounds to 3, while Chi(2) = 2.45266... rounds to 2.

Crossrefs

Cf. A383542.

Programs

  • Mathematica
    a[n_]:=Round[CoshIntegral[n]]; Array[a,31]

A383542 a(n) = round(Shi(n)) where Shi(x) is the sinh integral function.

Original entry on oeis.org

0, 1, 3, 5, 10, 20, 43, 96, 220, 519, 1246, 3036, 7480, 18599, 46596, 117478, 297780, 758319, 1938952, 4975454, 12807826, 33063593, 85572336, 221983185, 577057696, 1502975453, 3921470496, 10248248560, 26822559296, 70299597879, 184486604704, 484727787984
Offset: 0

Views

Author

Kritsada Moomuang, May 05 2025

Keywords

Comments

This sequence is almost the same as A383692, except at n = 0, where Chi(0) is undefined, and at n = 2, where Shi(2) = 2.50156... rounds to 3, while Chi(2) = 2.45266... rounds to 2.

Crossrefs

Cf. A383692.

Programs

  • Mathematica
    a[n_]:=Round[SinhIntegral[n]]; Array[a,31]

A377935 Decimal expansion of the area enclosed by the locus of the centroid of a Reuleaux triangle.

Original entry on oeis.org

0, 7, 9, 3, 2, 9, 5, 4, 7, 2, 8, 0, 7, 2, 5, 7, 1, 4, 6, 9, 6, 2, 8, 6, 0, 6, 3, 3, 7, 9, 7, 8, 5, 4, 4, 0, 1, 9, 6, 3, 3, 4, 7, 4, 5, 2, 5, 5, 6, 7, 5, 1, 7, 4, 2, 9, 0, 0, 5, 7, 9, 6, 4, 1, 9, 6, 5, 8, 2, 2, 6, 7, 4, 1, 7, 9, 1, 3, 0, 1, 1, 9, 2, 3, 1, 7, 3
Offset: 0

Views

Author

Kritsada Moomuang, Nov 11 2024

Keywords

Examples

			0.0793295472807257146962860633...

Links

Crossrefs

Cf. A066666.

Programs

  • Mathematica
    RealDigits[4 - 8/Sqrt[3] + (2*(Pi/9)), 10, 100, -1][[1]]

Formula

Equals 4 - 8/sqrt(3) + 2*Pi/9.
Equals (4/9)*(Pi - 3*A066666).

A377318 Numbers k such that prime(k), prime(k)+6, prime(k)+12, and prime(k)+18 are primes.

Original entry on oeis.org

3, 5, 13, 18, 54, 110, 116, 182, 234, 252, 271, 284, 351, 387, 464, 541, 551, 682, 709, 717, 741, 821, 829, 1171, 1417, 1448, 1510, 1594, 1711, 1726, 1842, 1853, 2009, 2086, 2209, 2297, 2408, 2600, 2680, 2876, 2924, 2930, 3253, 3303, 3437, 3977, 4384, 4431
Offset: 1

Views

Author

Kritsada Moomuang, Oct 24 2024

Keywords

Examples

			5 is in this sequence because: prime(5) = 11 and 11+6=17, 11+12=23, and 11+18=29 are all primes.

Links

Crossrefs

Cf. A000040, A000720, A023271.
Subsequence of A377317.

Programs

  • Mathematica
    Select[Range[1, PrimePi[50000]], PrimeQ[Prime[#] + 6] && PrimeQ[Prime[#] + 12] && PrimeQ[Prime[#] + 18] &]
Select[Range[4500],AllTrue[Prime[#]+{0,6,12,18},PrimeQ]&] (* Harvey P. Dale, Jun 17 2025 *)
  • PARI
    for(k=1, primepi(50000), p = prime(k); if(isprime(p+6) && isprime(p+12) && isprime(p+18), print(k)))

Formula

a(n) = pi(A023271(n)).

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