cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A234320 #16 Dec 14 2014 02:20:42
%S A234320 9,121,55,205,161
%N 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.
%C A234320 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.
%C A234320 n = 1: Dressler proved that 9 is the largest integer which is not the sum of distinct odd primes.
%C A234320 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.
%C A234320 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.
%C A234320 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.
%D A234320 A. Makowski, Partitions into unequal primes, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys., 8 (1960), 125-126.
%H A234320 R. E. Dressler, <a href="http://dx.doi.org/10.1090/S0002-9939-1972-0292746-6">A stronger Bertrand's postulate with an application to partitions</a>, Proc. Amer. Math. Soc., 33 (1972), 226-228.
%H A234320 R. E. Dressler, <a href="http://dx.doi.org/10.1090/S0002-9939-1973-0309842-8">Addendum to "A stronger Bertrand's postulate with an application to partitions"</a>, Proc. Am. Math. Soc., 38 (1973), 667.
%H A234320 R. E. Dressler, A. Makowski, and T. Parker, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0340206-6">Sums of Distinct Primes from Congruence Classes Modulo 12</a>, Math. Comp., 28 (1974), 651-652.
%H A234320 T. Kløve, <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0398969-0">Sums of Distinct Elements from a Fixed Set</a>, Math. Comp., 29 (1975), 1144-1149.
%e A234320 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.
%Y A234320 Cf. A231407, A231408.
%K A234320 nonn,more
%O A234320 1,1
%A A234320 _Jonathan Sondow_, Dec 28 2013