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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.
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
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
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
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