A106820 - OEIS

%I #8 Jul 12 2021 12:44:08

%S 2,3,5,41,131,191,193,223,311,317,397,461,593,599,641,821,823,881,

%T 1031,1091,1093,1097,1291,1297,1301,1321,1327,1451,1709,1871,2069,

%U 2081,2083,2179,2311,2351,2357,2551,2557,2579,2711,3163,3167,3251,3253,3257,3259

%N Smallest prime of the set of three consecutive primes whose sum of digits is a set of three distinct primes.

%H Harvey P. Dale, <a href="/A106820/b106820.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4)=41 is a term because sum of digits of three consecutive primes i.e. i.e. (41, 43, 47), whose sum of digits (i.e. 5, 7, 11)is a set of three distinct primes.

%t tdpQ[{a_,b_,c_}]:=Module[{d=Total[IntegerDigits[a]],e=Total[ IntegerDigits[ b]],f=Total[IntegerDigits[c]]},Length[Union[{d,e,f}]]==3&&AllTrue[ {d,e,f},PrimeQ]]; Select[Partition[Prime[ Range[ 500]],3,1],tdpQ][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 12 2021 *)

%K base,nonn

%O 1,1

%A _Shyam Sunder Gupta_, May 18 2005