A189571 - OEIS

%I #20 Sep 08 2022 08:45:56

%S 3,29,31,37,47,79,83,89,107,109,127,131,139,149,157,173,179,193,197,

%T 199,211,241,277,347,359,367,373,389,397,433,449,487,491,521,577,593,

%U 619,643,659,677,743,761,829,853,953,977,1049,1063,1087,1129,1151,1193

%N Smallest of nine consecutive primes whose sum is a prime.

%C First 7-tuple of consecutive primes belonging to the sequence: 118061, 118081, 118093, 118127, 118147, 118163, 118169. Twin primes in the sequence: 29, 31; 107, 109; 197, 199; 1427, 1429; 1607, 1609; 1721, 1723; 4019, 4021, etc. [_Bruno Berselli_, Aug 26 2013]

%H Bruno Berselli, <a href="/A189571/b189571.txt">Table of n, a(n) for n = 1..1000</a>

%e 47 is in the sequence because 47+53+59+61+67+71+73+79+83 = 593 and 593 is prime.

%t Transpose[Select[Partition[Prime[Range[500]],9,1],PrimeQ[Total[#]]&]] [[1]] (* _Harvey P. Dale_, Jun 05 2013 *)

%o (Magma) [ NthPrime(n): n in [1..190] | IsPrime(&+[NthPrime(n+s): s in [0..8]]) ];

%o (Python)

%o from sympy import isprime, nextprime

%o def aupto(limit):

%o   plst, alst = [3, 5, 7, 11, 13, 17, 19, 23, 29], []

%o   while plst[0] <= limit:

%o     if isprime(sum(plst)): alst.append(plst[0])

%o     plst = plst[1:] + [nextprime(plst[-1])]

%o   return alst

%o print(aupto(1200)) # _Michael S. Branicky_, Mar 29 2021

%Y Cf. A073681, A152468, A180948, A180950, A226380.

%K nonn

%O 1,1

%A _Bruno Berselli_, Apr 23 2011

%E Additional cross reference from _Harvey P. Dale_, Jun 05 2013