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A234320 Largest number that is not the sum of distinct primes of the form 2k+1, 4k+1, 4k+3, 6k+1, 6k+5, ...; or 0 if none exists. 1
9, 121, 55, 205, 161 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Largest number that is not the sum of distinct primes of the form 2nk+r for fixed n > 0 and 0 < r < 2n with gcd(2n,r) = 1.

n = 1: Dressler proved that 9 is the largest integer which is not the sum of distinct odd primes.

n = 2 and 3: Makowski proved that the largest integer that is not the sum of distinct primes of the form 4k+1, 4k+3, 6k+1, 6k+5 is 121, 55, 205, 161, respectively.

n = 6: Dressler, Makowski, and Parker proved that the largest integer that is not the sum of distinct primes of the form 12k+1, 12k+5, 12k+7, 12k+11 is 1969, 1349, 1387, 1475.

For n = 4, 5, 7, 8, 9, ..., the largest number that is not the sum of distinct primes of the form 2nk+r seems to be unknown.

REFERENCES

A. Makowski, Partitions into unequal primes, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys., 8 (1960), 125-126.

LINKS

Table of n, a(n) for n=1..5.

R. E. Dressler, A stronger Bertrand's postulate with an application to partitions, Proc. Amer. Math. Soc., 33 (1972), 226-228.

R. E. Dressler, Addendum to "A stronger Bertrand's postulate with an application to partitions", Proc. Am. Math. Soc., 38 (1973), 667.

R. E. Dressler, A. Makowski, and T. Parker, Sums of Distinct Primes from Congruence Classes Modulo 12, Math. Comp., 28 (1974), 651-652.

T. Kløve, Sums of Distinct Elements from a Fixed Set, Math. Comp., 29 (1975), 1144-1149.

EXAMPLE

The positive integers that are not the sum of distinct odd primes are A231408 = 1, 2, 4, 6, 9, so a(1) = A231408(5) = 9.

CROSSREFS

Cf. A231407, A231408.

Sequence in context: A214698 A024487 A002691 * A157930 A259836 A017102

Adjacent sequences:  A234317 A234318 A234319 * A234321 A234322 A234323

KEYWORD

nonn,more

AUTHOR

Jonathan Sondow, Dec 28 2013

STATUS

approved

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Last modified September 23 03:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)