The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#16 by N. J. A. Sloane at Sun Dec 14 02:20:42 EST 2014

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Fri Dec 12 11:47:08 EST 2014

STATUS

editing

proposed

Discussion

Fri Dec 12

11:50

Michel Marcus: For me ... yes, thanks.

#14 by Jon E. Schoenfield at Fri Dec 12 11:47:00 EST 2014

FORMULA

a(1) = A231408(5).

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.

Discussion

Fri Dec 12

11:47

Jon E. Schoenfield: Does this look okay?

#13 by Jon E. Schoenfield at Fri Dec 12 11:45:17 EST 2014

STATUS

proposed

editing

#12 by Michel Marcus at Fri Dec 12 10:26:27 EST 2014

STATUS

editing

proposed

Discussion

Fri Dec 12

11:45

Jon E. Schoenfield: Agreed.

#11 by Michel Marcus at Fri Dec 12 10:26:03 EST 2014

REFERENCES

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

LINKS

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.

Discussion

Fri Dec 12

10:26

Michel Marcus: Move formula to example ?

#10 by Michel Marcus at Fri Dec 12 10:22:56 EST 2014

LINKS

R. E. Dressler, <a href="http://wwwdx.amsdoi.org/journals/proc/1973-038-03/S0002-9939-1973-0309842-810.1090/S0002-9939-1973-0309842-8.pdf">Addendum to "A stronger Bertrand's postulate with an application to partitions"</a>, Proc. Am. Math. Soc., 38 (1973), 667.

R. E. Dressler, A. Makowski, and T. Parker, <a href="http://wwwdx.amsdoi.org/journals/mcom/1974-28-126/S0025-5718-1974-0340206-610.1090/S0025-5718-1974-0340206-6.pdf">Sums of Distinct Primes from Congruence Classes Modulo 12</a>, Math. Comp., 28 (1974), 651-652.

T. Kløve, <a href="http://wwwdx.amsdoi.org/journals/mcom/1975-29-132/S0025-5718-1975-0398969-010.1090/S0025-5718-1975-0398969-0.pdf">Sums of Distinct Elements from a Fixed Set</a>, Math. Comp., 29 (1975), 1144-1149.

STATUS

proposed

editing

#9 by Jon E. Schoenfield at Fri Dec 12 09:30:25 EST 2014

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Fri Dec 12 09:30:22 EST 2014

NAME

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.

COMMENTS

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.

LINKS

R. E. Dressler, <a href="http://www.ams.org/journals/proc/1973-038-03/S0002-9939-1973-0309842-8/S0002-9939-1973-0309842-8.pdf">Addendum to "A stronger Bertrand’'s postulate with an application to partitions"</a>, Proc. Am. Math. Soc., 38 (1973), 667.

T. Klove, Kløve, <a href="http://www.ams.org/journals/mcom/1975-29-132/S0025-5718-1975-0398969-0/S0025-5718-1975-0398969-0.pdf">Sums of Distinct Elements from a Fixed Set</a>, Math. Comp., 29 (1975), 1144-1149.

STATUS

approved

editing

#7 by Bruno Berselli at Tue Dec 31 14:36:19 EST 2013

STATUS

proposed

approved