A360497 - OEIS

%I #34 Mar 05 2023 19:49:45

%S 2,3,5,7,23,223,2777,7727,27527,33377,33773,35537,35573,35753,37337,

%T 52727,55337,55373,55733,73553,75227,75353,75533,222557,222773,223277,

%U 225257,225527,233357,235337,235553,253553,253733,277223,322727,323537,332573,335273

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

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

%e 2 is a term because it is a prime with prime digits only and its digit sum 2 is also a term.

%e 227 is not a term because the digit sum is 11 which is not a term because it has nonprime digits.

%e 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.

%p R:= {2,3,5,7}: count:= 4:

%p S:= [2,3,5,7];

%p for d from 2 to 11 do

%p   S:= map(t -> (10*t+2,10*t+3,10*t+5,10*t+7), S);

%p   for x in S do

%p     if member(convert(convert(x,base,10),`+`),R) and isprime(x) then

%p        R:= R union {x}; count:= count+1;

%p     fi

%p   od;

%p od:

%p sort(convert(R,list)); # _Robert Israel_, Mar 02 2023

%o (Python)

%o from sympy import isprime

%o seq = [2, 3, 5, 7]

%o for i in range(9, 10**6, 2):

%o     s = str(i)

%o     if set(s) <= set("2357") and sum(map(int, s)) in seq and isprime(i):

%o         seq.append(i)

%o print(seq)

%Y A subsequence of A062088.

%Y Cf. A000040, A007953.

%K nonn,base

%O 1,1

%A _Hongwei Jin_, Feb 09 2023