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

1,1

Links

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

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

Cf. A000040, A033447, A062088.

Sequence in context: A118922 A022464 A143828 * A142448 A257118 A244777

Adjacent sequences: A253137 A253138 A253139 * A253141 A253142 A253143

Keyword

nonn,base

Author

K. D. Bajpai, Dec 27 2014

Status

approved