A176603 - OEIS

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

(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: A050669 A362083 A322476 * A372807 A325902 A050715

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