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

1913, 98737, 35617, 1290719, 2030789, 11117213, 26742347, 109161617, 335440351, 92801029, 46006769, 3121826537, 5322398359, 7425894361, 6640450693, 43693080679, 53568812923, 72880315369, 271695323149, 40830835151, 38116957819, 241564332377, 351336577379, 551763092297, 923411678933

Offset: 1

Author

Klaus Brockhaus and Ki Punches, Aug 05 2009

Keywords

• base
• nonn

Comments

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.

Examples

			The smallest Ormiston pair with gap 18*3 is (35617, 35671), so a(3) = 35617.
		

Links

• Jens Kruse Andersen, Ormiston Tuples
• Eric Weisstein's World of Mathematics, Rearrangement Prime Pair

Crossrefs

Cf. A069567, A072274, A163678, A163679, A163680, A163681, A163682.

Programs

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))}

Extensions

Definition clarified by Klaus Brockhaus and Ki Punches, Aug 08 2009

a(17)-a(19) and a(22) from Klaus Brockhaus and Ki Punches, Aug 13 2009

a(23)-a(25) from Klaus Brockhaus, Sep 07 2009