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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 21 01:35 EDT 2021. Contains 343143 sequences. (Running on oeis4.)