A244311 - OEIS

%I #44 Jan 15 2023 18:40:26

%S 13,19,31,37,79,109,113,139,193,317,331,911,991,1453,1481,1669,1831,

%T 1901,7127,7561,7589,7687,9343,9413,9811,10223,11821,12889,13627,

%U 13633,16979,17551,32297,33529,34157,35747,37409,39521,39829,70957,71339,75653,79633,90289,94793,97583,99877

%N Primes (with d digits, say) that generate another prime when acted on by the "standard" superpermutation of length A007489(d) of d elements (cf. comment).

%C For primes with more than four digits, the sequence is based on the current information about the conjectured minimal length.

%C Since 2013 it is known that the superpermutations with minimal length are not unique for n > 4, and several ones are known for n = 5, cf. Wikipedia. Accordingly, the sequence is ill-defined if the choice of the superpermutation is not made precise. It also turns out that the 6-digit terms in the b-file correspond to the palindromic superpermutation of length A007489(d) obtained by the standard algorithm described on Wikipedia or Johnston's blog. For n = 5 this is of minimal length but only third in lexicographic order, for n >= 6 it is of non-minimal length. See A332088 for the analog sequence using the lexico-first superpermutation of minimal length and including the single-digit terms. - _M. F. Hasler_, Jul 28 2020

%C "Acted on" in the definition means that the digits of the prime are 'selected' according to those of the superpermutation. This sequence uses the palindromic superpermutations generated through the standard recursive algorithm, so the corresponding primes (with A007489(d) digits) are palindromic primes (A002385). - _M. F. Hasler_, Jul 29 2020

%H Abhiram R Devesh, <a href="/A244311/b244311.txt">Table of n, a(n) for n = 1..74</a>

%H Nathaniel Johnston, <a href="http://www.njohnston.ca/2013/04/the-minimal-superpermutation-problem/">Super Permutation</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Superpermutation">Superpermutation</a>

%e The super-permutation of 3 objects abc with minimal length is abcabacba.

%e p = 109 is in this sequence as under the super-permutation with minimal length, the number 109101901 is also prime.

%o From _M. F. Hasler_, Jul 29 2020: (Start)

%o (PARI) my(s); #SSP=vector(6,n,s=if(n--,my(t);concat([if(#Set(s)<n,[], s=concat([s,n+1,s]); forstep(i=min(#s,#t)-1,0,-1, if(s[1..1+i]==t[#t-i..#t],s=s[2+i..-1];break));t=s)|s<-[s[i+1..i+n]|i<-[0..#s-n]]]),[1])) \\ "standard" superpermutations up to n=6; see A332088 for those of minimal length

%o is_A244311(n)=ispseudoprime(fromdigits(vecextract(n=digits(n), SSP[#n])))

%o (A244311_upto(N)=select(is_A244311, primes([1,N])))(10^5) \\ (End)

%Y Cf. A007489, A002385, A180632, A332088.

%K nonn,base

%O 1,1

%A _Abhiram R Devesh_, Jun 25 2014

%E Definition corrected and keyword 'hard' removed; data and b-file double-checked by _M. F. Hasler_, Jul 29 2020