A167790 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,...)

3, 10, 3, 5, 8, 49, 13, 23, 23, 7, 39, 29, 15, 10, 39, 25, 30, 151, 38, 19, 139, 27, 174, 21, 287, 422, 240, 24, 94, 22, 16, 173, 861, 231, 143, 140, 213, 902, 18, 134, 143, 310, 70, 58, 295, 550, 237, 210, 229, 57, 221, 271, 194, 540, 145, 718, 116, 184, 90, 71, 168

Offset

1,1

Comments

It is conjectured that the sequence is infinite

If t is not restricted to nontrivial divisors, the sequence becomes A111287. - R. J. Mathar, Nov 17 2009

References

Richard E. Crandall and Carl Pomerance, Prime Numbers, Springer 2005

Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005)

Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996

Links

Table of n, a(n) for n=1..61.

Formula

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).

Example

(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;
(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;
(3) s(422)=2+3+5+...+2917=570145= 5 * 101 * 1129=5645*p(26) gives a(26)=422 and demonstrates the numerical difficulties.

Crossrefs

Cf. A007504 (sum of first n primes).

Cf. A167764.

Sequence in context: A124692 A091043 A321118 * A010708 A072988 A170855

Adjacent sequences: A167787 A167788 A167789 * A167791 A167792 A167793

Keyword

nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 12 2009, Nov 13 2009

Extensions

Extended by R. J. Mathar, Nov 17 2009

Status

approved