A114538 Transposition sequence of the dispersion of the primes.

1, 4, 6, 2, 8, 3, 7, 5, 11, 31, 9, 127, 17, 709, 5381, 52711, 13, 648391, 59, 9737333, 174440041, 3657500101, 277, 88362852307, 2428095424619, 75063692618249, 2586559730396077

Offset

1,2

Comments

A self-inverse permutation of the positive integers.

Links

Table of n, a(n) for n=1..27.

Neil Fernandez, An order of primeness, F(p)

Neil Fernandez, An order of primeness [cached copy, included with permission of the author]

Neil Fernandez, The Exploring Primeness Project

Robert G. Wilson v, The northwest corner of the Primeness array.

Formula

Suppose T is a rectangular array consisting of positive integers, each exactly once. The transposition sequence of T is here defined by placing T(i, j) in position T(j, i) for all i and j.

Example

Start with the northwest corner of T:
1 2 3 5 11 31 127 709 5381 52711 648391
4 7 17 59 277 1787 15299 167449 2269733 37139213 718064159
6 13 41 179 1063 8527 87803 1128889 17624813 326851121 7069067389
8 19 67 331 2221 19577 219613 3042161 50728129 997525853 22742734291
9 23 83 431 3001 27457 319211 4535189 77557187 1559861749 36294260117
10 29 109 599 4397 42043 506683 7474967 131807699 2824711961 64988430769
12 37 157 919 7193 72727 919913 14161729 259336153 5545806481 136395369829
a(1)=1 because 1=T(1,1) and T(1,1)=1.
a(2)=4 because 2=T(1,2) and T(2,1)=4.
a(3)=6 because 3=T(1,3) and T(3,1)=6.
a(13)=17 because 13=T(3,2) and T(2,3)=17.

Crossrefs

Cf. A114537.

Columns 1-6 above: A018252, A007821, A049078, A049079, A049080, A049081.

Rows 1-7 above: A007097, A057450, A057451, A057452, A057453, A057456, A057457.

Sequence in context: A066252 A065165 A088516 * A181096 A026239 A171547

Adjacent sequences: A114535 A114536 A114537 * A114539 A114540 A114541

Keyword

nonn

Author

Clark Kimberling, Dec 07 2005

Extensions

a(22)-a(27) from Robert G. Wilson v, Dec 24 2005

Status

approved