A360497 Maximal sequence of primes whose digits are primes and whose digit sum is also a term.

2, 3, 5, 7, 23, 223, 2777, 7727, 27527, 33377, 33773, 35537, 35573, 35753, 37337, 52727, 55337, 55373, 55733, 73553, 75227, 75353, 75533, 222557, 222773, 223277, 225257, 225527, 233357, 235337, 235553, 253553, 253733, 277223, 322727, 323537, 332573, 335273

Offset: 1

Author

Hongwei Jin, Feb 09 2023

Keywords

• nonn
• base

Comments

The sequence is maximal in the sense that a nonempty set of primes cannot be added consistently.

Examples

			2 is a term because it is a prime with prime digits only and its digit sum 2 is also a term.
227 is not a term because the digit sum is 11 which is not a term because it has nonprime digits.
27527 is a term: it is a prime, each digit (2,5,7) is also a prime, and the sum of the digits (2+7+5+2+7 = 23) is also in the sequence.
		

Crossrefs

A subsequence of A062088.

Cf. A000040, A007953.

Programs

Maple

R:= {2,3,5,7}: count:= 4:
S:= [2,3,5,7];
for d from 2 to 11 do
  S:= map(t -> (10*t+2,10*t+3,10*t+5,10*t+7), S);
  for x in S do
    if member(convert(convert(x,base,10),`+`),R) and isprime(x) then
       R:= R union {x}; count:= count+1;
    fi
  od;
od:
sort(convert(R,list)); # Robert Israel, Mar 02 2023

Python

from sympy import isprime
seq = [2, 3, 5, 7]
for i in range(9, 10**6, 2):
    s = str(i)
    if set(s) <= set("2357") and sum(map(int, s)) in seq and isprime(i):
        seq.append(i)
print(seq)