A176603 Smallest prime p of three consecutive primes (p,q,r) with p + q + r equal to a lower twin prime.
11, 17, 19, 83, 101, 281, 347, 349, 379, 401, 547, 641, 701, 839, 1103, 1151, 1171, 1187, 1279, 1303, 1409, 1439, 1489, 1823, 2089, 2243, 2857, 2861, 2927, 2999, 3083, 3203, 3347, 3359, 3467, 4639, 5087, 5233, 5861, 5879, 5881, 5923, 5953, 6007, 6299, 6491
Offset: 1
Keywords
Examples
11+13+17 = 41 = prime(13), 43 = prime(14), 11 is 1st term. 17+19+23 = 59 = prime(17), 61 = prime(18), 17 is 2nd term. Detailed list: 11+13+17 = 41, 17+19+23 = 59, 19+23+29 = 71, 83+89+97 = 269, 101+103+107 = 311, 281+283+293 = 857, 347+349+353 = 1049, 349+353+359 = 1061, 379+383+389 = 1151, 401+409+419 = 1229, 547+557+563 = 1667, 641+643+647 = 1931, 701+709+719 = 2129, 839+853+857 = 2549, 1103+1109+1117 = 3329, 1151+1153+1163 = 3467, 1171+1181+1187 = 3539, 1187+1193+1201 = 3581, 1279+1283+1289 = 3851, 1303+1307+1319 = 3929, 1409+1423+1427 = 4259, 1439+1447+1451 = 4337, 1489+1493+1499 = 4481, 1823+1831+1847 = 5501, 2089+2099+2111 = 6299, 2243+2251+2267 = 6761, 2857+2861+2879 = 8597, 2861+2879+2887 = 8627, 2927+2939+2953 = 8819, 2999+3001+3011 = 9011.
References
- Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005.
- Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Band I, B. G. Teubner, Leipzig u. Berlin, 1909.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1 and vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
Programs
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Mathematica
Prime /@ Position[Plus @@@ Partition[ Prime[ Range[1000]], 3, 1] , ?(PrimeQ[#]&&PrimeQ[#+2] &)]//Flatten (* _Amiram Eldar, Dec 24 2019 *)
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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
Extensions
keyword:base removed, and sequence extended by R. J. Mathar, Apr 23 2010
Comments