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 1-6 of 6 results.

A090547 Leading entries in triangle in A090548 and A113470.

Original entry on oeis.org

1, 2, 3, 5, 5, 7, 35, 635, 635, 199, 3841, 3841, 4979, 2995, 13561, 22903, 1691, 5951, 72697, 72697, 72697, 172151, 172151, 1782371, 1782371
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

Different from A087308.
In case there was more than one solution with minimum A090548(n), the one with minimum stride A090549(n) was selected to generate A090547(n) and A090549(n). - R. J. Mathar, Apr 28 2007

Crossrefs

Cf. A087308, A090548, A090549, A113470.

Formula

A090548(n)=a(n)+(n-1)*A090549(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007
More terms from David Wasserman, Jan 08 2006, May 11 2007
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007

A090549 Common difference of arithmetic progression in n-th row of A090548 and A113470.

Original entry on oeis.org

1, 1, 2, 6, 6, 30, 30, 72, 72, 210, 132, 132, 114, 594, 48
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

In case there was more than one solution with minimum A090548(n), the one with minimum stride A090549(n) was selected to generate A090547(n) and A090549(n). - R. J. Mathar, Apr 28 2007

Crossrefs

Cf. A087308, A090547, A090548, A113470.

Formula

A090548(n)=A090547(n)+(n-1)*a(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007

A086786 Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same prime signature.

Original entry on oeis.org

1, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 481, 485, 489, 493, 497, 501, 505, 635, 707, 779, 851, 923, 995, 1067, 1139, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 3841
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2003

Keywords

Comments

In this sequence "smallest" means that the last term of the arithmetic progression is minimized. A113460 minimizes the first term.

Examples

			Triangle begins:
1
2,3
3,5,7
5,11,17,23
5,11,17,23,29
7,37,67,97,127,157
481,485,489,493,497,501,505
635,707,779,851,923,995,1067,1139
635,707,779,851,923,995,1067,1139,1211
199,409,619,829,1039,1249,1459,1669,1879,2089
...

Links

Crossrefs

A087310 contains the corresponding common differences, A087308 the initial terms, A087309 the final terms.
Cf. A087308, A087309, A087310, A114660, A114663, A114670.
Row 10 is the same for A113470, A133276, A133277 and listed as A033168.

Extensions

Edited and extended by David Wasserman, Jan 08 2006
Further edits by N. J. A. Sloane, Oct 17 2007

A133276 Triangle read by rows: row n gives the first arithmetic progression of n primes with minimal distance, cf. A033188.

Original entry on oeis.org

2, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 7, 157, 307, 457, 607, 757, 907, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 60858179, 60860489, 60862799, 60865109, 60867419, 60869729, 60872039, 60874349, 60876659, 60878969, 60881279
Offset: 1

Views

Author

N. J. A. Sloane, Oct 17 2007

Keywords

Comments

The first 10 rows (i.e., 55 terms) are the same as for A133277 (where the final term is minimal), but here a(56) = T(11,1) = 608581797 while A133277(11,1) = 110437. - M. F. Hasler, Jan 02 2020

Examples

			Triangle begins:
    2
    2   3
    3   5   7
    5  11  17  23
    5  11  17  23   29
    7  37  67  97  127  157
    7 157 307 457  607  757  907
  199 409 619 829 1039 1249 1459 1669
  199 409 619 829 1039 1249 1459 1669 1879
  199 409 619 829 1039 1249 1459 1669 1879 2089
  ...
Row 10 is the same as in A086786, A113470, A133277, and listed as A033168. - _M. F. Hasler_, Jan 02 2020

Links

Crossrefs

For common differences see A033188, for initial terms see A033189.
Different from A133277 (from T(11,1) = a(56) on).
Cf. A086786, A113470, A033168.

Programs

  • Maple
    AP:=proc(i,d,l) [seq(i + (j-1)*d, j=1..l )]; end;

A033168 Longest arithmetic progression of primes with difference 210 and minimal initial term.

Original entry on oeis.org

199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089
Offset: 0

Views

Author

Manuel Valdivia, Apr 22 1998

Keywords

Comments

Since 210 == 1 (mod 11), a progression of primes with difference 210 can't have more than ten terms because there is exactly one multiple of 11 within each run of eleven consecutive terms. For example, 2089 + 210 = 2299 = 11^2 * 19. - Alonso del Arte, Dec 22 2017, edited by M. F. Hasler, Jan 02 2020
After 199, the next prime which starts a CPAP-10 with common gap 210 is 243051733. See A094220 for further starting points. - M. F. Hasler, Jan 02 2020

References

  • Paul Glendinning, Math in Minutes: 200 Key Concepts Explained in an Instant. New York, London: Quercus (2013): pp. 316-317.
  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 143.

Links

Crossrefs

Row 10 of A086786, A113470, A133276, A133277.
Cf. A094220.

Programs

  • Mathematica
    199 + 210*Range[0, 9] (* Paolo Xausa, Sep 14 2024 *)
  • PARI
    forprime(p=1,,for(i=1,9,isprime(p+i*210)||next(2)); return([p+d|d<-[0..9]*210])) \\ M. F. Hasler, Jan 02 2020

Formula

a(n) = a(0) + n*210 for 0 <= n <= 9. - M. F. Hasler, Jan 02 2020

A090548 Least number that ends an arithmetic progression of n numbers with the same number of divisors.

Original entry on oeis.org

1, 3, 7, 23, 29, 157, 215, 1139, 1211, 2089, 5161, 5293, 6347, 10717, 14233, 28213, 31451, 72965, 119029, 121603, 124177, 611261, 632171, 2003171, 2012771
Offset: 1

Views

Author

Amarnath Murthy, Dec 09 2003

Keywords

Comments

In the following triangle the n-th row contains the least set of n numbers in arithmetic progression with the same number of divisors. By "least" we mean that the largest term is minimized. Sequence contains the leading diagonal. In other words, largest of n numbers in arithmetic progression with the same tau function, or 0 if no such number exists.

Examples

			Triangle (A113470) begins:
1
2 3
3 5 7
5 11 17 23
5 11 17 23 29 ...

Crossrefs

Leading diagonal of A113470.
Cf. A087309, A096003, A113470, A087308, A090547, A090549.

Formula

a(n)=A090547(n)+(n-1)*A090549(n). - R. J. Mathar, Apr 28 2007

Extensions

Corrected and extended by R. J. Mathar, Apr 28 2007
More terms from David Wasserman, Jan 08 2006, May 11 2007
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 11 2007
Showing 1-6 of 6 results.

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