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 1-4 of 4 results.

A135026 Values B(n) associated with the stationary terms listed in A135025.

Original entry on oeis.org

7, 26, 81, 270, 841, 2480, 7479, 22404, 66535, 197470, 592419, 1772034, 5317217, 15955046, 47860367, 143540614, 430579631, 1291494336, 3874347869, 11622575710, 34869569547, 104608356834, 313820413899, 941454837836, 2824364840671, 8473084264392, 25419236780193, 76257724291584
Offset: 1

Views

Author

Lior Deutsch (liorde(AT)gmail.com), Feb 10 2008

Keywords

Examples

			B(4)=7 is the first stationary term of B, so a(1) = 7.
		

Extensions

New term added Lior Deutsch (liorde(AT)gmail.com), Oct 17 2008
a(17)-a(28) from Giovanni Resta, Oct 02 2019

A145842 a(n) = prime(A135025(n)).

Original entry on oeis.org

7, 23, 79, 269, 839, 2477, 7477, 22397, 66533, 197453, 592393, 1772033, 5317217, 15955019, 47860361, 143540597, 430579631, 1291494329, 3874347863, 11622575663, 34869569509, 104608356781, 313820413861, 941454837811, 2824364840663, 8473084264373, 25419236780191, 76257724291547
Offset: 1

Views

Author

Lior Deutsch (liorde(AT)gmail.com), Oct 21 2008

Keywords

Crossrefs

Cf. A135025.

Formula

a(n) = A000040(A135025(n)). - Amiram Eldar, Apr 06 2020

Extensions

a(17)-a(28) calculated from the data at A135025 by Amiram Eldar, Apr 06 2020

A309226 Index of n-th low point in A008348 (see Comments for definition).

Original entry on oeis.org

0, 3, 8, 21, 56, 145, 366, 945, 2506, 6633, 17776, 48521, 133106, 369019, 1028404, 2880287, 8100948, 22877145, 64823568, 184274931, 525282740, 1501215193, 4299836186, 12340952049, 35486796312, 102220582465, 294917666854, 852123981581, 2465458792768
Offset: 0

Views

Author

N. J. A. Sloane, Sep 01 2019

Keywords

Comments

A "low point" in a sequence is a term which is less than the previous term (this condition is skipped for the initial term) and which is followed by two or more increases.
This concept is useful for the analysis of sequences (such as A005132, A008344, A008348, A022837, A076042, A309222, etc.) which have long runs of terms which alternately rise and fall.

Crossrefs

Programs

  • Maple
    blocks := proc(a,S) local b,c,d,M,L,n;
    # Given a list a, whose leading term has index S, return [b,c,d], where b lists the indices of the low points in a, c lists the values of a at the low points, and d lists the length of runs between the low points.
    b:=[]; c:=[]; d:=[]; L:=1;
    # is a[1] a low point?
       n:=1;
       if( (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
       b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi;
    for n from 2 to nops(a)-2 do
    # is a[n] a low point?
       if( (a[n-1]>a[n]) and (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then
       b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi; od;
    [b,c,d]; end;
    # Let a := [0, 2, 5, 0, 7, 18, 5, 22, 3, 26, 55, 24, ...]; be a list of the first terms in A008348
    blocks(a,0)[1]; # the present sequence
    blocks(a,0)[2]; # A324782
    blocks(a,0)[3]; # A324783

Formula

a(n) = A135025(n-1)-1.

Extensions

a(17)-a(28) from Giovanni Resta, Oct 02 2019
Modified definition to make offset 0. - N. J. A. Sloane, Oct 02 2019

A324783 First differences of A309226: distances in A008348 from n-th low point to the next.

Original entry on oeis.org

3, 5, 13, 35, 89, 221, 579, 1561, 4127, 11143, 30745, 84585, 235913, 659385, 1851883, 5220661, 14776197, 41946423, 119451363, 341007809, 975932453, 2798620993, 8041115863, 23145844263, 66733786153, 192697084389, 557206314727, 1613334811187
Offset: 0

Views

Author

N. J. A. Sloane, Sep 01 2019

Keywords

Comments

Also (essentially) the first differences of A135025.
See A309226 for more information.

Crossrefs

Programs

Extensions

a(16)-a(27) from Giovanni Resta, Oct 02 2019
Modified definition to make offset 0. - N. J. A. Sloane, Oct 02 2019
Showing 1-4 of 4 results.