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.

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A159580 Integral quotients occur consecutively this many times (in sequence associated with A051838 and A116536).

Original entry on oeis.org

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

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Author

Enoch Haga, Apr 16 2009

Keywords

Examples

			a(1)=2 because the 1st subsequence (38,39) of consecutive integers has run length 2.
a(2)=3 because the 2nd subsequence is (56,57,58) which has run length 3.
a(3)=2 because the 3rd subsequence is (167,168) which has run length 2.

Crossrefs

Cf. A051838, A116536, A140763, A159578, A159581.

Extensions

Recomputed based on b-file of A051838. - R. J. Mathar, Aug 28 2018

A159639 Last divisors at which integral quotients occur consecutively.

Original entry on oeis.org

154, 2183, 4002, 8635, 19203, 93017, 96298, 122414, 166762, 182090, 201354, 241237, 337645, 346495, 406813, 456729, 574678, 668811, 781635, 799006, 929442, 952150, 1014194, 1379625, 1455259, 1513549, 1558110, 1573089, 1938354, 2028842
Offset: 1

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Author

Enoch Haga, Apr 17 2009, Apr 21 2009

Keywords

Comments

Considering dividend/divisor=quotient, in a(1) of A116536, A159578, and A159579, 3=30/10; sometimes integral quotients appear n times in succession -- see A159580 where a(3)indicates that 5 integral quotients appear one after another. A159581 and A159639 give the first and last values of the divisors producing these integral quotients.
Many of the associated sequences submitted by this author were wrong. Should be recomputed. The UBASIC program should be regarded with suspicion. - N. J. A. Sloane, Oct 02 2011.

Examples

			a(1)=154 because it is the last or second of two divisors (125 being the first) where integral quotients are produced in succession (one after the other): 5577321750/125=44618574, integral; and 161742330750/154=1050274875, integral. See a(4) in A116536, A159578, and A159579.

Crossrefs

Cf. A116536, A159578 A159579 A159580 A159581

Programs

  • UBASIC
    10 'product of cons primes divided by sum cons primes 20 N=3:Q=2*N:R=R+N:R=R+2 30 A=3:S=sqrt(N) 40 B=N/A 50 if int(B)*A=N then 110 60 A=A+2:if A
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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