A253140 Smallest of three consecutive primes in arithmetic progression with common difference 24 and digit sum prime.

89, 373, 773, 863, 1279, 2063, 2089, 2399, 2663, 2753, 3299, 4153, 4373, 5879, 6173, 6263, 6779, 7079, 7499, 7853, 9473, 10453, 11399, 12253, 12479, 14699, 16763, 19379, 21163, 21563, 25073, 29363, 32189, 33599, 40063, 41879, 42773, 50053, 50363, 52673, 56453

Offset: 1

Author

K. D. Bajpai, Dec 27 2014

Keywords

• nonn
• base

Examples

			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.
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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A033447, A062088.

Programs

Mathematica

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
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 *)