sequences that are permutations

John Layman layman at
Tue Oct 23 17:01:27 CEST 2001

N. J. A. Sloane writes:
> Howard Landman <howard at> has put together a preliminary
> list of the sequences that are permutations of the natural numbers
> (or in some cases of the nonnegative integers).
> Here is the current version.  If anyone knows of other examples,
> please send them to me (njas).
> The entries in the index will also be updated.
> Sequence-Inverse	
> A000027	- self-inverse
> A002251	- self-inverse	
> A003100	- self-inverse	
> A003188	- A006068
> A004484	- A064206	
> A004485	- A064207	
> A004486	- A064208	
> A004487	- A064211	
> A019444	- self-inverse	
> A026243	- self-inverse	
> A029654	- A064360	
> A064413 - A064664
> A032447	- A064275	
> A035312	- A035358
> A035506	- A064357	
> A035513	- A064274	
> A047708	- A048850	
> A048647	- A064212	
> A048672	- A064273	
> A048673	- A064216	
> A048679	- A048680	
> A052330	- A064358	
> A059900 - A059884
> A052331	- A064359	
> A054238	- A054239	
> A054424	- A054426	
> A054427	- A054428	
> A054429	- self-inverse	
> A054430	- self-inverse	
> A054081	- n/a		array: rows are permutations but it isn't itself

I have checked the July 2000 version of the EIS (the latest that I have
downloaded) and found the following list of 251 sequences that satisfy the two
conditions: (1) no term occurs twice, and (2) at least the first twenty natural
numbers 1-20 occur. These sequences are thus candidates for the permutation
sequences sought by njas.  Some of these can be easily confirmed and some easily
disproved but, anyway, here they are.

Some of the sequences in the preliminary list (above) do not appear because
fewer than twenty terms were found.

The numbers in brackets give the range of consecutive integers found, starting
with 0 or 1.

John Layman

A004491[0-56]     A004483[0-68]     A049084[1-24]     
A027656[1-35]     A004490[0-56]     A004482[0-59]     
A035043[0-68]     A048212[1-20]     A055176[1-45]     
A014681[1-68]     A026262[1-51]     A026234[1-25]     
A054082[1-51]     A026255[1-47]     A026190[1-31]     
A026204[1-40]     A054084[1-50]     A026205[1-32]     
A026214[1-33]     A026221[1-33]     A026243[1-39]     
A002251[0-41]     A026191[1-41]     A050137[1-31]     
A047708[0-54]     A026215[1-42]     A026220[1-42]     
A048850[0-53]     A004488[0-29]     A026252[1-24]     
A004443[0-55]     A006015[0-63]     A054425[1-33]     
A030542[1-28]     A000027[1-77]     A001477[0-77]     
A033619[0-87]     A055643[0-59]     A044923[1-48]     
A002837[0-40]     A044922[1-35]     A032513[0-31]     
A048266[1-31]     A004441[1-29]     A004438[1-29]     
A032521[0-25]     A044921[1-24]     A050608[1-24]     
A046510[0-24]     A048242[1-23]     A004830[0-22]     
A038770[1-22]     A032517[0-22]     A032520[0-20]     
A034837[1-20]     A051108[0-20]     A051107[0-20]     
A003100[0-49]     A026267[1-52]     A055170[0-48]     
A005941[1-22]     A026266[1-51]     A056018[0-55]     
A056017[0-65]     A032447[1-40]     A054582[1-20]     
A026264[1-51]     A048201[1-24]     A026265[1-51]     
A014321[1-36]     A055265[1-72]     A054426[1-20]     
A054424[1-35]     A048673[1-36]     A054077[1-56]     
A026194[1-33]     A026260[1-45]     A054076[1-56]     
A036552[1-51]     A026259[1-48]     A026195[1-43]     
A004515[0-24]     A056019[0-31]     A034701[1-52]     
A054239[0-43]     A048680[0-33]     A035513[1-29]     
A026167[1-32]     A054238[0-52]     A048679[0-30]     
A054427[1-36]     A026166[1-42]     A026257[1-45]     
A026182[1-32]     A026198[1-32]     A026206[1-32]     
A038776[1-42]     A026202[1-32]     A004517[0-48]     
A026200[1-32]     A026218[1-32]     A004519[0-27]     
A036130[1-30]     A036129[1-29]     A026258[1-47]     
A026183[1-41]     A026199[1-41]     A026207[1-41]     
A050171[1-25]     A026201[1-41]     A026219[1-41]     
A050138[1-23]     A026203[1-42]     A050125[1-20]     
A052194[1-20]     A051242[1-28]     A036164[0-21]     
A055179[1-45]     A004468[0-63]     A004444[0-55]     
A048647[1-63]     A035044[0-68]     A054086[1-57]     
A054068[1-57]     A054069[1-56]     A004442[0-67]     
A054430[1-71]     A026098[1-23]     A006369[0-39]     
A054089[1-51]     A006368[1-40]     A038722[1-47]     
A003188[0-31]     A006042[1-31]     A026137[1-34]     
A026173[1-34]     A026187[1-34]     A026211[1-34]     
A019444[1-32]     A006068[0-35]     A054429[1-63]     
A026136[1-41]     A026172[1-41]     A026186[1-41]     
A026210[1-41]     A055456[1-71]     A026245[1-38]     
A026178[1-31]     A026197[1-31]     A026217[1-31]     
A004484[0-60]     A004492[0-53]     A055173[1-42]     
A026248[1-38]     A026253[1-24]     A026184[1-31]     
A026208[1-31]     A026193[1-33]     A026143[1-35]     
A026188[1-41]     A026212[1-41]     A055266[1-72]     
A026250[1-24]     A034175[0-31]     A050129[1-32]     
A055182[1-46]     A026246[1-40]     A026177[1-41]     
A026196[1-41]     A026216[1-41]     A026189[1-33]     
A026213[1-33]     A026185[1-41]     A026209[1-41]     
A026192[1-40]     A026142[1-44]     A050128[1-30]     
A055115[0-24]     A020703[1-64]     A004485[0-57]     
A004493[0-53]     A004445[0-55]     A026239[1-26]     
A055185[1-51]     A026247[1-39]     A050001[1-29]     
A036165[0-27]     A004486[0-60]     A004494[0-53]     
A055116[0-35]     A004446[0-55]     A036173[0-29]     
A050132[1-23]     A055117[0-48]     A004447[0-55]     
A004495[0-54]     A004487[0-57]     A004448[0-55]     
A055118[0-63]     A004496[0-53]     A004497[0-53]     
A004449[0-49]     A004450[0-49]     A004498[0-53]     
A050133[1-20]     A004451[0-47]     A004499[0-53]     
A004500[0-53]     A004452[0-47]     A004453[0-47]     
A004501[0-53]     A004454[0-47]     A004502[0-53]     
A004503[0-53]     A004455[0-47]     A004456[0-47]     
A004504[0-53]     A004505[0-53]     A004457[0-41]     
A036171[0-51]     A004506[0-53]     A004458[0-41]     
A002252[1-26]     A008575[1-20]     A004459[0-39]     
A004507[0-53]     A036170[0-45]     A004460[0-39]     
A004508[0-53]     A004509[0-53]     A004461[0-39]     
A004462[0-39]     A004510[0-53]     A004463[0-39]     
A004511[0-53]     A004512[0-53]     A004464[0-39]     
A036166[0-29]     A004513[0-53]     A004465[0-33]     
A036167[0-35]     A036168[0-39]     A036169[0-41]     
A036172[0-57]     A038459[1-25]     A056561[0-39]     
A056534[1-39]     A056535[1-34]     A056539[0-63]     
A056537[1-42]     A056536[1-43]     

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