A371361 The first of two consecutive primes p, q such that p, q and p + q are all pandigital.

10234568791, 10234685971, 10234756849, 10234786589, 10234865779, 10235678449, 10237845649, 10243756981, 10245836789, 10245936781, 10245968371, 10247658389, 10247658923, 10247685893, 10248357659, 10248756893, 10256734879, 10256839447, 10256839477, 10257384679, 10257486913, 10258367429, 10258367489

Offset: 1

Author

Robert Israel, Mar 19 2024

Keywords

• nonn
• base

Comments

The first case where a(n) and a(n+1) are consecutive primes is n = 18. Thus p = a(18) = 10256839447, q = a(19) = 10256839477 and r = 10256839487 are three consecutive primes with p, q, r, p + q and q + r all pandigital. In addition, p + r = 20513678934 ia pandigital.

Examples

			a(3) =  10234756849 is a term because it is prime and pandigital, the next prime 10234756859 is also pandigital, and  10234756849 + 10234756859 = 20469513708 is pandigital.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..100 from Robert Israel)

Crossrefs

Cf. A171102, A050288

Programs

Maple

ispd:= proc(n) convert(convert(n,base,10),set) = {$0..9} end proc:
q:=nextprime(10^10): qgood:= false: Res:= NULL: count:= 0:
while count < 25 do
  p:= q; pgood:= qgood;
  q:= nextprime(p); qgood:= ispd(q);
  if pgood and qgood and ispd(p+q) then
    Res:= Res, p; count:= count+1;
  fi;
od:
Res;