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A007414 Largest number not a sum of distinct primes >= prime(n).
(Formerly M4080)
2
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 (list; graph; refs; listen; history; text; internal format)
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 A025493 A091519

Adjacent sequences:  A007411 A007412 A007413 * A007415 A007416 A007417

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 23 14:06 EDT 2018. Contains 316528 sequences. (Running on oeis4.)