[seqfan] 9-digit accepting integers

[Eric Angelini]

Hello SeqFans,

21123 has the property that every pair of adjacent digits sum to a prime number

(thus belonging to https://oeis.org/A182175).

We want to transform this integer into another integer having the same property

by inserting single digits somewhere:



21123 + 0 = 211230

21123 + 1 = 121123

21123 + 2 = 211232

21123 + 3 = 321123

21123 + 4 = 211234

21123 + 5 = 521123

21123 + 6 = 216123

21123 + 7 = impossible

21123 + 8 = 211238

21123 + 9 = 921123



I think no integer will ever accept the 10 digits from 0 to 9.

Is 21123 the smallest accepting 9 digits? What are the others

(like 41123, accepting 7 now, but not 5)?



Best,

É.