A259603 -id:A259603 - cp's OEIS frontend

A259429 With a(1) = 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a cube.

1, 15, 39, 89, 161, 271, 415, 17, 37, 91, 159, 273, 413, 19, 35, 93, 157, 275, 411, 21, 33, 95, 155, 277, 409, 23, 31, 97, 153, 279, 407, 25, 29, 99, 151, 281, 405, 27, 101, 149, 283, 403, 621, 65, 63, 187, 245, 5, 11, 43, 85, 165, 267, 419, 13, 3, 51, 77, 173, 259, 427, 597, 861, 163, 87, 41, 209, 223, 463, 561, 125

Offset: 1

Derek Orr, Jun 26 2015

Believed to be a permutation of the odd integers.
A259603(n) = (a(n) + a(n+1)) / 2; a(A259537(n)) = 2*n-1. - Reinhard Zumkeller, Jun 30 2015
The scatter-plot shows interesting helix-like lenticular structures. - Antti Karttunen, May 29 2016

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A259260, A086517, A175428.
Cf. A010057, A005408, A259537.
Cf. A259603, A259565, A259542.

import Data.List (delete)
a259429 n = a259429_list !! (n-1)
a259429_list = 1 : f 1 [3, 5 ..] where
   f x zs = g zs where
     g (y:ys) = if a010057 ((x + y) `div` 2) == 1
                   then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Jun 29 2015

a = {1}; Do[k = 1; While[Or[MemberQ[a, k], !IntegerQ@ Power[Mean[{a[[i - 1]], k}], 1/3]], k++]; AppendTo[a, k], {i, 2, 120}]; a (* Michael De Vlieger, May 29 2016 *)

v=[1]; n=1; while(#v<200, s=(n+v[#v])/2; if(type(s)=="t_INT", if(ispower(s,3)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0)); n++); v

A259602 (A259260(n) + A259260(n+1)) / 2.

Original entry on oeis.org

4, 9, 16, 25, 16, 4, 9, 16, 25, 36, 25, 16, 25, 36, 49, 64, 81, 100, 64, 16, 25, 36, 49, 64, 81, 64, 36, 49, 64, 81, 100, 81, 64, 81, 100, 121, 144, 169, 196, 144, 64, 100, 144, 81, 36, 49, 64, 81, 64, 49, 64, 81, 100, 121, 144, 169, 144, 121, 100, 64, 81

Offset: 1

Reinhard Zumkeller, Jun 30 2015

nonn

All terms are squares by definition of A259260.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A259260, A000290, A086517, A259603, A259604, A259605.

a259602 n = a259602_list !! (n-1)
a259602_list = zipWith ((flip div 2 .) . (+))
                       a259260_list $ tail a259260_list

A259604 (A259542(n) + A259542(n+1)) / 2.

Original entry on oeis.org

3, 6, 10, 15, 10, 6, 10, 15, 21, 28, 36, 45, 36, 28, 36, 45, 55, 36, 21, 28, 36, 45, 36, 28, 36, 45, 55, 66, 78, 91, 78, 66, 78, 91, 105, 78, 55, 66, 78, 91, 78, 66, 78, 91, 105, 120, 136, 153, 120, 78, 91, 105, 91, 78, 66, 78, 105, 120, 136, 153, 171, 153

Offset: 1

Reinhard Zumkeller, Jun 30 2015

nonn

All terms are triangular numbers by definition of A259542.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A259542, A000217, A086517, A259602, A259603, A259605.

a259604 n = a259604_list !! (n-1)
a259604_list = zipWith ((flip div 2 .) . (+))
                       a259542_list $ tail a259542_list

A259605 (A259565(n) + A259565(n+1)) / 2.

Original entry on oeis.org

2, 5, 6, 7, 10, 13, 14, 15, 19, 22, 21, 22, 26, 29, 30, 31, 34, 37, 38, 39, 42, 46, 47, 46, 51, 53, 55, 58, 55, 57, 62, 65, 66, 67, 70, 73, 74, 77, 79, 78, 82, 86, 85, 86, 91, 94, 93, 94, 101, 102, 101, 102, 105, 110, 109, 110, 114, 118, 119, 118, 122, 127

Offset: 1

Reinhard Zumkeller, Jun 30 2015

nonn

All terms are squarefree by definition of A259565.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A259565, A005117, A086517, A259602, A259603, A259604.

a259605 n = a259605_list !! (n-1)
a259605_list = zipWith ((flip div 2 .) . (+))
                       a259565_list $ tail a259565_list

A086518 Primes arising as the arithmetic mean of a pair of successive terms of A086517.

Original entry on oeis.org

2, 5, 11, 13, 17, 29, 31, 23, 29, 41, 37, 41, 53, 59, 61, 53, 59, 73, 71, 73, 83, 89, 97, 101, 97, 89, 97, 109, 113, 127, 131, 137, 131, 127, 131, 127, 137, 149, 157, 163, 173, 181, 167, 157, 167, 173, 181, 191, 193, 197, 211, 223, 229, 223, 211, 223, 241, 227, 223

Offset: 1

Amarnath Murthy, Jul 30 2003

nonn

			2 = (1+3)/2, 11 = (7+15)/2, etc.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A086517, A259602, A259603, A259604, A259605.

a086518 n = a086518_list !! (n-1)
a086518_list = zipWith ((flip div 2 .) . (+))
                       a086517_list $ tail a086517_list
-- Reinhard Zumkeller, Jun 30 2015

v=[1]; n=1; while(n<100, s=(n+v[#v])/2; if(type(s)=="t_INT", if(isprime(s)&&!vecsearch(vecsort(v), n), print1(s,", "); v=concat(v, n); n=0)); n++) \\ Derek Orr, Jun 16 2015

a(n) = (A086517(n)+A086517(n+1))/2. - David Wasserman, Mar 10 2005

More terms from David Wasserman, Mar 10 2005

cp's OEIS Frontend

A259429 With a(1) = 1, a(n) is the smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a cube.

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A259602 (A259260(n) + A259260(n+1)) / 2.

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A259604 (A259542(n) + A259542(n+1)) / 2.

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A259605 (A259565(n) + A259565(n+1)) / 2.

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A086518 Primes arising as the arithmetic mean of a pair of successive terms of A086517.

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