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A253140
Smallest of three consecutive primes in arithmetic progression with common difference 24 and digit sum prime.
4
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
1,1
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
K. D. Bajpai, Dec 27 2014
STATUS
approved