The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A176603 Smallest prime p of three consecutive primes (p,q,r) with p + q + r equal to a lower twin prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is constructed by intersecting A034961 and A001359, then printing the smallest of the three primes that sum to A034961. 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. EXAMPLE 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. MATHEMATICA Prime /@ Position[Plus @@@ Partition[ Prime[ Range[1000]], 3, 1] , _?(PrimeQ[#]&&PrimeQ[#+2] &)]//Flatten  (* Amiram Eldar, Dec 24 2019 *) PROG (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 CROSSREFS Cf. A001359, A034961, A174454. Sequence in context: A245622 A050669 A322476 * A325902 A050715 A006618 Adjacent sequences:  A176600 A176601 A176602 * A176604 A176605 A176606 KEYWORD nonn AUTHOR Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 21 2010 EXTENSIONS keyword:base removed, and sequence extended by R. J. Mathar, Apr 23 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 18 15:59 EST 2020. Contains 332019 sequences. (Running on oeis4.)