cp's OEIS Frontend

A163863 a(n) = smaller member p of first (i.e., smallest) Ormiston pair (p, q) with gap 18*n.

%I A163863 #14 Feb 16 2025 08:33:11
%S A163863 1913,98737,35617,1290719,2030789,11117213,26742347,109161617,
%T A163863 335440351,92801029,46006769,3121826537,5322398359,7425894361,
%U A163863 6640450693,43693080679,53568812923,72880315369,271695323149,40830835151,38116957819,241564332377,351336577379,551763092297,923411678933
%N A163863 a(n) = smaller member p of first (i.e., smallest) Ormiston pair (p, q) with gap 18*n.
%C A163863 An Ormiston pair (or rearrangement prime pair) is a pair of consecutive primes that use the same digits in a different order. The gap q - p of an Ormiston pair (p, q) is a multiple of 18.
%H A163863 Jens Kruse Andersen, <a href="http://primerecords.dk/ormiston_tuples.htm">Ormiston Tuples</a>
%H A163863 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RearrangementPrimePair.html">Rearrangement Prime Pair</a>
%e A163863 The smallest Ormiston pair with gap 18*3 is (35617, 35671), so a(3) = 35617.
%o A163863 (PARI) {m=20; v=vector(m); p=1; while(p<10^10, q=nextprime(p+1); gap=q-p; if(gap%18==0&&v[j=gap\18]==0&&vecsort(Vec(Str(p)))==vecsort(Vec(Str(q))), v[j]=p; print(p, ",", q, ",", gap, ",")); p=q); print(); for(j=1, m, if(v[j]>0, print1(v[j], ","), break))}
%Y A163863 Cf. A069567, A072274, A163678, A163679, A163680, A163681, A163682.
%K A163863 base,nonn
%O A163863 1,1
%A A163863 _Klaus Brockhaus_ and _Ki Punches_, Aug 05 2009
%E A163863 Definition clarified by _Klaus Brockhaus_ and _Ki Punches_, Aug 08 2009
%E A163863 a(17)-a(19) and a(22) from _Klaus Brockhaus_ and _Ki Punches_, Aug 13 2009
%E A163863 a(23)-a(25)  from _Klaus Brockhaus_, Sep 07 2009