A227113 -id:A227113 - cp's OEIS frontend

A227288 Greatest common divisor of consecutive terms in A227113.

1, 2, 1, 3, 1, 5, 1, 7, 2, 4, 3, 3, 1, 11, 1, 13, 2, 2, 1, 17, 1, 19, 2, 4, 3, 3, 1, 23, 1, 5, 2, 4, 1, 29, 1, 31, 1, 3, 1, 5, 1, 37, 1, 3, 1, 41, 1, 43, 2, 4, 3, 5, 1, 47, 1, 7, 1, 3, 2, 4, 1, 53, 1, 5, 1, 3, 1, 59, 1, 61, 2, 2, 1, 67, 2, 2, 1, 3, 1, 71, 1

Offset: 1

Reinhard Zumkeller, Jul 05 2013

nonn

a(n) = GCD(A227113(n),A227113(n+1));
a(2*n) > 1 by definition of A227113;
9 is the smallest odd number m with a(m) > 1: a(9) = GCD(A227113(9),A227113(10)) = GCD(14,8) = 2;
a(A227289(n)) = n and a(m) <> n for m < A227289(n).

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

a227288 n = a227288_list !! (n-1)
a227288_list = zipWith gcd (tail a227113_list) a227113_list

A227114 Inverse permutation to A227113.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 8, 10, 12, 7, 14, 11, 16, 9, 13, 18, 20, 19, 22, 24, 26, 15, 28, 25, 30, 17, 27, 32, 34, 31, 36, 33, 38, 21, 40, 39, 42, 23, 44, 41, 46, 45, 48, 50, 52, 29, 54, 51, 56, 53, 58, 60, 62, 59, 64, 57, 66, 35, 68, 61, 70, 37, 67, 72, 65, 73, 74

Offset: 1

Reinhard Zumkeller, Jul 01 2013

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

import Data.List (elemIndex); import Data.Maybe (fromJust)
a227114 = (+ 1) . fromJust . (`elemIndex` a227113_list)

A227289 Smallest m such that gcd(A227113(m+1), A227113(m)) = n.

Original entry on oeis.org

1, 2, 4, 10, 6, 177, 8, 514, 500, 349, 14, 4791, 16, 5949, 1623, 863, 20, 2629, 22, 5113, 2043, 3211, 28, 7347, 4593, 11911, 1647, 12819, 34, 27325, 36, 15755, 34527, 29319, 5459, 2797, 42, 24535, 20145, 15511, 46, 26523, 48, 64895, 13335, 40769, 54, 43835, 184041

Offset: 1

Reinhard Zumkeller, Jul 05 2013

nonn

A227288(a(n)) = n and A227288(m) <> n for m < a(n).

			.   n |   a(n) | A227288(a(n)) = gcd(A227113(a(n)),A227113(a(n)+1))
.  ---+--------+--------------- -----------------------------------
.   1 |     1  |            1  =  gcd(1,2)
.   2 |     2  |            2  =  gcd(2,4)
.   3 |     4  |            3  =  gcd(3,6)
.   4 |    10  |            4  =  gcd(8,12)
.   5 |     6  |            5  =  gcd(5,10)
.   6 |   177  |            6  =  gcd(168,162)
.   7 |     8  |            7  =  gcd(7,14)
.   8 |   514  |            8  =  gcd(472,480)
.   9 |   500  |            9  =  gcd(459,468)
.  10 |   349  |           10  =  gcd(330,320)
.  11 |    14  |           11  =  gcd(11,22)
.  12 |  4791  |           12  =  gcd(4524,4512)

import Data.List (elemIndex); import Data.Maybe (fromJust)
a227289 = (+ 1) . fromJust . (`elemIndex` a227288_list)

cp's OEIS Frontend

A227288 Greatest common divisor of consecutive terms in A227113.

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A227114 Inverse permutation to A227113.

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A227289 Smallest m such that gcd(A227113(m+1), A227113(m)) = n.

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