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A381855 Starting from prime(n), a(n) is the minimum number > 1 of consecutive primes whose sum is the lesser of a twin prime pair.

%I A381855 #27 Mar 23 2025 16:46:05
%S A381855 2,95,317,23,3,5,3,3,277,7,7,25,35,237,7,5,17,41,15,33,23,7,3,111,257,
%T A381855 3,7,57,5,11,57,13,11,79,45,67,29,97,11,15,15,21,113,19,35,15,9,5,123,
%U A381855 29,59,27,19,227,223,37,279,53,41,3,135,53,143,81,41,29,39,63
%N A381855 Starting from prime(n), a(n) is the minimum number > 1 of consecutive primes whose sum is the lesser of a twin prime pair.
%H A381855 Abhiram R Devesh, <a href="/A381855/b381855.txt">Table of n, a(n) for n = 1..10000</a>
%e A381855 a(1) = 2 because we need to add the primes 2 and 3, to reach the lesser of the twin prime pair (5 and 7).
%o A381855 (Python)
%o A381855 import sympy
%o A381855 def a(n):
%o A381855    p=sympy.prime(n);s=p;c=1
%o A381855    p=sympy.nextprime(p);s+=p;c+=1
%o A381855    while not(sympy.isprime(s)and sympy.isprime(s+2)):p=sympy.nextprime(p);s+=p;c+=1
%o A381855    return c
%o A381855 (PARI) a(n) = my(p=prime(n), q=nextprime(p+1), s = p+q, k=2); while (!(isprime(s) && isprime(s+2)), q=nextprime(q+1); s+=q; k++); k; \\ _Michel Marcus_, Mar 09 2025
%Y A381855 Cf. A001359.
%K A381855 nonn
%O A381855 1,1
%A A381855 _Abhiram R Devesh_, Mar 08 2025