|
%I #12 Sep 16 2016 13:52:52
%S 89,373,773,863,1279,2063,2089,2399,2663,2753,3299,4153,4373,5879,
%T 6173,6263,6779,7079,7499,7853,9473,10453,11399,12253,12479,14699,
%U 16763,19379,21163,21563,25073,29363,32189,33599,40063,41879,42773,50053,50363,52673,56453
%N Smallest of three consecutive primes in arithmetic progression with common difference 24 and digit sum prime.
%H K. D. Bajpai, <a href="/A253140/b253140.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 89: 89 + 24 = 113; 113 + 24 = 137; all three are prime. Their digit sums 8+9 = 17, 1+1+3 = 5 and 1+3+7 = 11 are also prime.
%e a(2) = 373: 373 + 24 = 397; 397 + 24 = 421; all three are prime. Their digit sums 3+7+3 = 13, 3+9+7 = 19 and 4+2+1 = 7 are also prime.
%t A253140 = {}; Do[d = 24; k = Prime[n]; k1 = k+d; k2 = k+2d; If[PrimeQ[k1] && PrimeQ[k2] && PrimeQ[Plus@@IntegerDigits[k]] && PrimeQ[Plus@@IntegerDigits[k1]] && PrimeQ[Plus@@IntegerDigits[k2]], AppendTo[A253140,k]], {n,20000}]; A253140
%t tcpQ[n_]:=Module[{a=n+24,b=n+48},AllTrue[{a,b},PrimeQ]&&AllTrue[Total/@ (IntegerDigits/@{n,a,b}),PrimeQ]]; Select[Prime[Range[6000]],tcpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 16 2016 *)
%Y Cf. A000040, A033447, A062088.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Dec 27 2014
|
