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.

A121492 Gaps associated with A002540(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 20, 22, 30, 32, 34, 36, 44, 52, 72, 86, 96, 112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282, 288, 292, 320, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490, 500, 514, 516, 532, 534, 540, 582, 588, 602
Offset: 1

Views

Author

Lekraj Beedassy, Aug 03 2006

Keywords

Comments

Record gaps between prime powers (A000961) [Michael B. Porter, Nov 01 2009].

Examples

			6 is in the sequence since 53 and 59 are consecutive prime powers and no smaller pair of consecutive prime powers differ by 6 or more. [From _Michael B. Porter_, Nov 03 2009]

Links

  • Jan Kristian Haugland, Table of n, a(n) for n = 1..87 (terms 1..79 from _Donovan Johnson_). The extra terms are copied from A005250 as the associated prime gaps do not contain any prime powers.

Crossrefs

Cf. A002540, A167236, A057820, A000961 [Michael B. Porter, Nov 01 2009]
start of gap: A002540, end of gap: A167236, gaps: A057820 [From Michael B. Porter, Nov 03 2009]

Programs

  • PARI
    isA000961(n) = (omega(n) == 1 || n == 1)
d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(d); d_max=d);n_prev=n)) /* Michael B. Porter, Nov 01 2009 */

Extensions

Second term corrected. a(20)-a(79) and b-file from Donovan Johnson, Nov 14 2008

A094158 Erroneous version of A002540.

Original entry on oeis.org

1, 2, 5, 13, 19, 32, 53, 89, 139, 199, 293, 887, 1129, 1331, 5591, 8467, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353
Offset: 1

Views

Author

Keywords

References

  • J. P. Gram, Undersoegelser angaaende maengden af primtal under en given graense, Det Kongelige Danskevidenskabernes Selskabs Skrifter, series 6, vol. 2 (1884), 183-288; see p. 255.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Entry 565, Academic Press, 1973.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Entry M1431, Academic Press, 1995.

A167236 Larger prime power associated with gaps in A121492.

Original entry on oeis.org

2, 7, 16, 23, 37, 59, 97, 149, 211, 307, 907, 1151, 1361, 5623, 8501, 9587, 15727, 19661, 31469, 156007, 360749, 370373, 492227, 1349651, 1357333, 2010881, 4652507, 17051887, 20831533, 47326913, 122164969, 189695893, 191913031, 387096383, 436273291, 1294268779
Offset: 1

Views

Author

Michael B. Porter, Nov 01 2009, Nov 03 2009

Keywords

Examples

			59 is in the sequence since 53 and 59 are consecutive prime powers with a difference of 6 and no smaller pair of consecutive prime powers differ by 6 or more.

Links

  • Jan Kristian Haugland, Table of n, a(n) for n = 1..87. The extra terms after a(33) are copied from A000101 as the associated prime gaps do not contain any prime powers.

Crossrefs

Size of gap: A121492
Smaller prime power (start of gap): A002540
Gaps between prime powers: A057820
List of prime powers: A000961

Programs

  • PARI
    isA000961(n) = (omega(n) == 1 || n == 1)
d_max=0;n_prev=1;for(n=2,1e6,if(isA000961(n),d=n-n_prev;if(d>d_max,print(n);d_max=d);n_prev=n))

Extensions

a(34) onwards from Jan Kristian Haugland, Oct 18 2024

A121493 Start of the smallest m-string of equal entries in A003418(n)=lcm(1,2,...,n), where m=A121492.

Original entry on oeis.org

2, 60, 360360, 232792560, 144403552893600, 164249358725037825439200, 71876675494548945530447225706507529440, 33312720618553145840562713089120360606823375590405920630576000
Offset: 1

Views

Author

Lekraj Beedassy, Aug 03 2006

Keywords

Crossrefs

Cf. A002540.

A316191 List of indices where the maximum of {A316190(j) | j<=n} increases.

Original entry on oeis.org

1, 11, 37, 89, 211, 1344, 1345, 1346, 2503, 3967, 15704, 15705, 16033, 19634, 19635, 24281, 31428, 31429, 31430, 31431, 31432, 31433, 38501, 58831, 155964, 203713, 206699
Offset: 1

Views

Author

Peter Luschny, Jun 26 2018

Keywords

Examples

			a(3) = 37 because A316190(37) = 4 > 2 = max{A316190(n) : 1 <= n < 37}.

Crossrefs

Cf. A002540, A316190.

Programs

  • Maple
    A316191_list := proc(N) local R,a,A,n,mx; R := NULL;
A := A316190_list(N); n := 1; mx := 0;
for a in A do
   if a > mx then mx := a; R := R,n fi;
   n := n + 1;
od; [R] end:
A316191_list(10000);
Showing 1-5 of 5 results.

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

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