A071196 - OEIS

%I #16 Nov 17 2020 23:11:49

%S 5,127,23,31,41,101,59,71,83,97,109,479,131,263,431,173,331,199,211,

%T 223,421,251,269,719,757,311,827,587,349,647,683,1367,733,439,457,811,

%U 487,503,2141,1747,941,5009,991,1951,607,2053,661,1151,21139,701,1753

%N The sum of the sequence starting with prime(n) and having prime sum defined in A071194, or -1 if no such sequence exists.

%H Rémy Sigrist, <a href="/A071196/b071196.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A071196/a071196.png">Colored logarithmic scatterplot of the first 10000 terms</a> (where the color is function of A071194(n))

%e n=25: prime(25)=97, sum=97+101+103+107+109+113+127=757=a(25), prime; shorter (length>1) partial sums are composite: {97,198,301,408,517,630,757}.

%t Table[sm = Prime[k] + Prime[k + 1]; g = 1; While[ ! PrimeQ[sm], g++; sm = sm + Prime[k + g]]; sm, {k, 1, 51}] (* _Lei Zhou_, Dec 02 2005 *)

%o (PARI) { forprime (p=2, prime(51), s=p; forprime (q=p+1, oo, if (isprime(s+=q), print1 (s", "); break))) } \\ _Rémy Sigrist_, Nov 17 2020

%Y Cf. A000040, A071194, A071195, A071197, A071198.

%K nonn,look

%O 1,1

%A _Labos Elemer_, May 16 2002

%E Edited and escape clause added by _N. J. A. Sloane_, Nov 17 2020~