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
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.
Programs
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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)
Comments