A007414 Largest number not a sum of distinct primes >= prime(n). (Formerly M4080)

6, 9, 27, 45, 45, 57, 75, 81, 87, 105, 123, 135, 135, 165, 169, 189, 195, 209, 231, 237, 267, 267, 267, 315, 315, 333, 345, 363, 369, 405, 411, 429, 441, 465, 483, 485, 525, 525, 535, 555, 579, 579, 609, 611, 645, 657, 687, 705, 715, 717, 721

Offset

1,1

Comments

Kløve conjectures that a(n) ~ 3p where p is the n-th prime. This implies the (binary) Goldbach conjecture for large enough n. - Charles R Greathouse IV, Apr 03 2012

References

Torleiv Kløve, Sums of distinct primes. Nordisk Mat. Tidskr. 21 (1973), pp. 138-140.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 73.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Prog

(PARI) issum(n, x)=if(isprime(n), return(n>=x)); if(if(n%2, n<3*x, n<2*x), return(!n)); forprime(p=x, n-if(n%2, 2*x, x), if(issum(n-p, p+1), return(1))); 0
a(n)=my(p=prime(n), k=2*p-2, lower=k, upper=2*k+2); while(upper>lower, if(issum(upper, p), upper--, lower=2*k+2; k=upper; upper=2*k+2)); k \\ Charles R Greathouse IV, Apr 03 2012

Crossrefs

Cf. A180306.

Sequence in context: A243708 A300345 A024878 * A274977 A340630 A025493

Adjacent sequences: A007411 A007412 A007413 * A007415 A007416 A007417

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved