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

1,1

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.

Links

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

Example

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.

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;

Crossrefs

Cf. A171102, A050288

Sequence in context: A098143 A276590 A259152 * A135047 A017541 A357609

Adjacent sequences: A371358 A371359 A371360 * A371362 A371363 A371364

Keyword

nonn,base

Author

Robert Israel, Mar 19 2024

Status

approved