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A176603 Smallest prime p of three consecutive primes (p,q,r) with p + q + r equal to a lower twin prime.

%I A176603 #21 Dec 24 2019 08:27:12
%S A176603 11,17,19,83,101,281,347,349,379,401,547,641,701,839,1103,1151,1171,
%T A176603 1187,1279,1303,1409,1439,1489,1823,2089,2243,2857,2861,2927,2999,
%U A176603 3083,3203,3347,3359,3467,4639,5087,5233,5861,5879,5881,5923,5953,6007,6299,6491
%N A176603 Smallest prime p of three consecutive primes (p,q,r) with p + q + r equal to a lower twin prime.
%C A176603 The sequence is constructed by intersecting A034961 and A001359, then printing the smallest of the three primes that sum to A034961.
%D A176603 Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005.
%D A176603 Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Band I, B. G. Teubner, Leipzig u. Berlin, 1909.
%H A176603 Amiram Eldar, <a href="/A176603/b176603.txt">Table of n, a(n) for n = 1..10000</a>
%H A176603 E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, <a href="http://name.umdl.umich.edu/ABV2766.0001.001">vol. 1</a> and <a href="http://name.umdl.umich.edu/ABV2766.0002.001">vol. 2</a>, Leipzig, Berlin, B. G. Teubner, 1909.
%e A176603 11+13+17 = 41 = prime(13), 43 = prime(14), 11 is 1st term.
%e A176603 17+19+23 = 59 = prime(17), 61 = prime(18), 17 is 2nd term.
%e A176603 Detailed list:
%e A176603 11+13+17 = 41, 17+19+23 = 59, 19+23+29 = 71, 83+89+97 = 269,
%e A176603 101+103+107 = 311, 281+283+293 = 857, 347+349+353 = 1049,
%e A176603 349+353+359 = 1061, 379+383+389 = 1151, 401+409+419 = 1229,
%e A176603 547+557+563 = 1667, 641+643+647 = 1931, 701+709+719 = 2129,
%e A176603 839+853+857 = 2549, 1103+1109+1117 = 3329, 1151+1153+1163 = 3467,
%e A176603 1171+1181+1187 = 3539, 1187+1193+1201 = 3581, 1279+1283+1289 = 3851,
%e A176603 1303+1307+1319 = 3929, 1409+1423+1427 = 4259, 1439+1447+1451 = 4337,
%e A176603 1489+1493+1499 = 4481, 1823+1831+1847 = 5501, 2089+2099+2111 = 6299,
%e A176603 2243+2251+2267 = 6761, 2857+2861+2879 = 8597, 2861+2879+2887 = 8627,
%e A176603 2927+2939+2953 = 8819, 2999+3001+3011 = 9011.
%t A176603 Prime /@ Position[Plus @@@ Partition[ Prime[ Range[1000]], 3, 1] , _?(PrimeQ[#]&&PrimeQ[#+2] &)]//Flatten  (* _Amiram Eldar_, Dec 24 2019 *)
%o A176603 (PARI) my(ppp=2,pp=3); forprime(p=5,6600,my(psum=ppp+pp+p); if(isprime(psum)&&isprime(psum+2), print1(ppp,", ")); ppp=pp; pp=p) \\ _Hugo Pfoertner_, Dec 24 2019
%Y A176603 Cf. A001359, A034961, A174454.
%K A176603 nonn
%O A176603 1,1
%A A176603 Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 21 2010
%E A176603 keyword:base removed, and sequence extended by _R. J. Mathar_, Apr 23 2010