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 1-5 of 5 results.

A129484 Primes of the form 17k + 1.

Original entry on oeis.org

103, 137, 239, 307, 409, 443, 613, 647, 919, 953, 1021, 1123, 1259, 1327, 1361, 1429, 1531, 1667, 1871, 1973, 2143, 2347, 2381, 2551, 2687, 2789, 2857, 3061, 3163, 3299, 3469, 3571, 3673, 3877, 3911, 4013, 4217, 4421, 4523, 4591, 4931, 4999, 5101, 5237
Offset: 1

Views

Author

Cino Hilliard, May 29 2007

Keywords

Links

Crossrefs

Cf. A140544, A092074, A094657, A138623, A140545, A138629, A138633, A138631, A138627, A140542, A138625, A141865, A140540, A140543, A140541.

Programs

  • Magma
    [n: n in [1..5000 by 17] | IsPrime(n)] ; // Vincenzo Librandi, Apr 04 2011
  • Mathematica
    Select[Range[1,5000,17],PrimeQ[#]&] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2011 *)
  • PARI
    cicadayear(n) = forstep(x=1,n,17,if(isprime(x),print1(x",")))

A138631 Primes of the form 17*k + 9.

Original entry on oeis.org

43, 179, 281, 349, 383, 587, 757, 859, 1063, 1097, 1301, 1471, 1607, 1709, 1777, 1811, 1879, 1913, 2083, 2287, 2389, 2423, 2593, 2729, 2797, 3001, 3137, 3307, 3511, 3613, 3851, 3919, 4021, 4157, 4259, 4327, 4463, 4871, 4973, 5279, 5347, 5381, 5449, 5483
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 14 2008

Keywords

Examples

			17*2 + 9 = 43, 17*10 + 9 = 179, 17*16 + 9 = 281, 17*20 + 9 = 349, 17*22 + 9 = 349, ...

Links

Crossrefs

Cf. A138632.
Primes congruent to k mod 17: A129484 (k=1), A140544 (k=2), A092074 (k=3), A094657 (k=4), A138623 (k=5), A140545 (k=6), A138629 (k=7), A138633 (k=8), this sequence (k=9), A138627 (k=10), A140542 (k=11), A138625 (k=12), A141865 (k=13), A140540 (k=14), A140543 (k=15), A140541 (k=16).

Programs

  • Mathematica
    a={};Do[x=17*n+9;If[PrimeQ[x],AppendTo[a,x]],{n,10^2}];a
Select[17*Range[350]+9,PrimeQ] (* Harvey P. Dale, May 14 2017 *)

Formula

From A.H.M. Smeets, Sep 05 2019: (Start)
a(n)/log(a(n)) ~ 16*n;
Integral_{x=2..a(n)} dx/log(x) ~ 16*n. (End)

Extensions

More terms from N. J. A. Sloane, Jul 11 2008

A138633 Primes of the form 17*k - 9.

Original entry on oeis.org

59, 127, 229, 263, 331, 433, 467, 569, 739, 773, 977, 1181, 1249, 1283, 1453, 1487, 1657, 1759, 1861, 1997, 2099, 2269, 2371, 2473, 2609, 2677, 2711, 3119, 3187, 3221, 3323, 3391, 3527, 3697, 3833, 4003, 4139, 4241, 4513, 4547, 4649, 4751, 5023, 5227, 5261
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, May 14 2008

Keywords

Examples

			17*4 - 9 = 59, 17*8 - 9 = 127, 17*14 - 9 = 229, 17*16 - 9 = 263, 17*20 - 9 = 331, 17*26 - 9 = 433, 17*28 - 9 = 467, ...

Links

Crossrefs

Cf. A138634.
Primes congruent to k mod 17: A129484 (k=1), A140544 (k=2), A092074 (k=3), A094657 (k=4), A138623 (k=5), A140545 (k=6), A138629 (k=7), this sequence (k=8), A138631 (k=9), A138627 (k=10), A140542 (k=11), A138625 (k=12), A141865 (k=13), A140540 (k=14), A140543 (k=15), A140541 (k=16).

Programs

  • Mathematica
    a={};Do[x=17*n-9;If[PrimeQ[x],AppendTo[a,x]],{n,10^2}];a
Select[17*Range[400]-9,PrimeQ] (* Harvey P. Dale, Jul 25 2020 *)

Formula

From A.H.M. Smeets, Sep 05 2019: (Start)
n ~ (1/16) * a(n)/log(a(n)).
n ~ (1/16) * Integral_{x=2..a(n)} dx/log(x). (End)

Extensions

More terms from N. J. A. Sloane, Jul 11 2008

A240136 Prime numbers in the Antikythera mechanism.

Original entry on oeis.org

19, 53, 127, 223
Offset: 1

Views

Author

Michel Lagneau, Apr 02 2014

Keywords

Comments

The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the 2nd Century B.C. This device is a sophisticated arrangement of bronze gears, which can calculate the relative positions of the Sun and Moon, lunar phases and even eclipses. It is conjectured that it could also calculate the positions of the inner planets, but this is unproven. It was recovered from a Roman shipwreck in 1900 as a corroded mass of gear work. Detailed analysis could only really begin once X-ray equipment became available. Scans performed over the last 20 years have added significant clues as to the function and operation of the device. Ratios of gear tooth counts in the device indicate a good match to ratios used by the ancients to calculate the dates of eclipses using the Saros and Metonic cycles. Fragments of text recovered from the device mention the sun and moon and use month names used by the Greek city of Corinth and its colonies.
To understand the origin of these numbers, it is necessary to introduce other fundamental constants such as 365, 254, 235.
365: number of days in the Egyptian calendar. The X-ray scan of this zodiac fragment showed a ring of 365 holes.
Prime 19: number of years of the Meton cycle. The number 19 = 38/2 where 38 is the numbers of teeth in corresponding wheel of the mechanism. 19 years = 254 tropical months, and also 19 years = 235 synodic months.
235: Metonic constant or synodic months. There are 235 lunar months every 19 years that are arranged on a spiral.
Prime 223: 223 synodic months (or the Saros eclipse cycle), where 223 is the numbers of teeth counted in a wheel of the mechanism.
Prime 127 = Metonic cycle/2 = 254/2. The Moon appears to return to the same point in the sky relative to the zodiac in a sidereal month, and in 19 years there are 235 + 19 = 254 sidereal months. So, 127 is the numbers of teeth counted in a wheel of the mechanism.
Prime 53 = a gear-count which appears thrice in the device.
Remark: three primes 19, 53 and 223 are of the form 17*n+2 (A140544).

References

  • Price, D. de S. Gears from the Greeks: The Antikythera Mechanism — A Calendar Computer from ca. 80 BC, Trans Am. Philos. Soc., New Series, 64, Part 7 (reprinted as Science History Publications, NY 1975), (1974)
  • Wright, M.T. Epicyclic Gearing and the Antikythera Mechanism, Part I, Antiquarian Horology, Vol. 27 No. 3, pp. 270279, March (2003)
  • Wright, M.T. Epicyclic Gearing and the Antikythera Mechanism, Part I, Antiquarian Horology, Vol. 27 No. 3, pp. 270279, March (2003)
  • Wright, M.T. The Antikythera Mechanism and the Early History of the MoonPhase Display, Antiquarian Horology, Volume 29, No.3, March 2006, pp. 319329, (2006)
  • Wright, M.T. Understanding the Antikythera Mechanism, Proceedings 2nd International Conferenceon Ancient Greek Technology, Technical Chamber of Greece, Athens, pp 4960, (2006)
  • Freeth, T. The Antikythera Mechanism: 1. Challenging the Classic Research, Mediterranean Archaeology & Decoding the Antikythera Mechanism, published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). Archaeometry, Vol. 2 No. 1, pp. 2135, (2002)

Links

A267693 Decimal expansion of 477/4237.

Original entry on oeis.org

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

Views

Author

Omar E. Pol, Jan 24 2016

Keywords

Comments

In the Antikythera mechanism this constant represents the difference between the time it takes for the moon to return to perigee and the time it takes for the moon to come back to the same point in the zodiac, in a year's turn.
The discovery that the constant 0.112579655 is present in the Antikythera mechanism is due to Tony Freeth.
The prime numbers 19, 53, 127 and 223 are related to the number of teeth of some of the known 30 bronze gearwheels of the mechanism (see A240136).
The prime numbers 19, 53 and 223 appear in the formula of this constant. They are also the first three primes congruent to 19 mod 34 (see A142072), or in other words: the first three odd primes of the form 17*n+2 (see A140544).
The function of one or two gears with 63 teeth is unknown.
Note that in ancient astronomy a cycle of 126 days was known to be related to Mercury and also a cycle of 13*19 + 5 = 252 days related to Venus; both 126 and 252 are multiples of 63.

Examples

			0.11257965541656832664621194241208402171347651640311541...

Links

Crossrefs

Cf. A000040, A140544, A142072, A240136.

Programs

Formula

d = (18/223)*(53/38) = (9/223)*(53/19) = 477/4237.
Showing 1-5 of 5 results.

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

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