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%I #10 Dec 14 2021 12:13:12
%S 3,10,3,5,8,49,13,23,23,7,39,29,15,10,39,25,30,151,38,19,139,27,174,
%T 21,287,422,240,24,94,22,16,173,861,231,143,140,213,902,18,134,143,
%U 310,70,58,295,550,237,210,229,57,221,271,194,540,145,718,116,184,90,71,168
%N a(n) is the index k of k-th prime p(k) in the smallest sum s(k)=2+3+...+p(k)=t*p(n) of first k primes where t is a true divisor and first occurrence of factor p(n) (n=1,2,3,...)
%C It is conjectured that the sequence is infinite
%C If t is not restricted to nontrivial divisors, the sequence becomes A111287. - _R. J. Mathar_, Nov 17 2009
%D Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer 2005
%D Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005)
%D Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996
%F a(n) = min[2+3+...+p(k)/t], where the minimum is taken with respect to k, the denominator t > 1 is an integer divisor of numerator s(k)=2+3+...+p(k).
%e (1) s(5)=2+3+5+7+11=28=2^2*7=4*p(4) gives a(4)=5 as first occurrence of prime factor p(4)=7;
%e (2) s(8)=2+3+5+7+11+13+17+19=77=7*11=7*p(5) gives a(5)=8 as first occurrence of prime factor p(5)=11;
%e (3) s(422)=2+3+5+...+2917=570145= 5 * 101 * 1129=5645*p(26) gives a(26)=422 and demonstrates the numerical difficulties.
%Y Cf. A007504 (sum of first n primes).
%Y Cf. A167764.
%K nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 12 2009, Nov 13 2009
%E Extended by _R. J. Mathar_, Nov 17 2009
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