The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A352296 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A352296

Smallest number that can be expressed as the sum of two primes in exactly n ways or -1 if no such number exists.
(history; published version)

#11 by R. J. Mathar at Sun Mar 20 12:15:17 EDT 2022

STATUS

editing

approved

#10 by R. J. Mathar at Sun Mar 20 12:15:06 EDT 2022

CROSSREFS

Essentially the same as A023036 and A001172.

STATUS

approved

editing

#9 by N. J. A. Sloane at Sun Mar 13 19:14:08 EDT 2022

STATUS

proposed

approved

#8 by Ilya Gutkovskiy at Fri Mar 11 14:45:05 EST 2022

STATUS

editing

proposed

#7 by Ilya Gutkovskiy at Fri Mar 11 14:44:55 EST 2022

CROSSREFS

Essentially the same as A023036.

#6 by Ilya Gutkovskiy at Fri Mar 11 14:44:27 EST 2022

CROSSREFS

Essentially the same as A023036

STATUS

proposed

editing

#5 by Amiram Eldar at Fri Mar 11 14:30:00 EST 2022

STATUS

editing

proposed

#4 by Amiram Eldar at Fri Mar 11 14:29:58 EST 2022

MATHEMATICA

f[n_] := Count[IntegerPartitions[n, {2}], _?(And @@ PrimeQ[#] &)]; seq[max_] := Module[{s = Table[0, {max}], n = 1, c = 0, k}, While[c < max, k = f[n]; If[k < max && s[[k + 1]] == 0, c++; s[[k + 1]] = n]; n++]; s]; seq[50] (* Amiram Eldar, Mar 11 2022 *)

STATUS

proposed

editing

#3 by Chai Wah Wu at Fri Mar 11 14:19:37 EST 2022

STATUS

editing

proposed

#2 by Chai Wah Wu at Fri Mar 11 10:18:08 EST 2022

NAME

allocated for Chai Wah WuSmallest number that can be expressed as the sum of two primes in exactly n ways or -1 if no such number exists.

DATA

1, 4, 10, 22, 34, 48, 60, 78, 84, 90, 114, 144, 120, 168, 180, 234, 246, 288, 240, 210, 324, 300, 360, 474, 330, 528, 576, 390, 462, 480, 420, 570, 510, 672, 792, 756, 876, 714, 798, 690, 1038, 630, 1008, 930, 780, 960, 870, 924, 900, 1134, 1434, 840, 990, 1302

OFFSET

0,2

COMMENTS

Conjecture: a(n) != -1 for all n.

If n > 0 and a(n) != -1, then a(n) is even.

a(0) = A014092(1)

a(1) = A067187(1)

a(2) = A067188(1)

a(3) = A067189(1)

a(4) = A067190(1)

a(5) = A067191(1)

a(6) = A066722(1)

a(7) = A352229(1)

a(8) = A352230(1)

a(9) = A352231(1)

a(10) = A352233(1)

PROG

(Python)

from itertools import count

from sympy import nextprime

def A352296(n):

if n == 0:

return 1

pset, plist, pmax = {2}, [2], 4

for m in count(2):

if m > pmax:

plist.append(nextprime(plist[-1]))

pset.add(plist[-1])

pmax = plist[-1]+2

c = 0

for p in plist:

if 2*p > m:

break

if m - p in pset:

c += 1

if c == n:

return m

CROSSREFS

Cf. A014092, A067187, A067188, A067189, A067190, A067191, A066722, A352229, A352230, A352231, A352233.

KEYWORD

allocated

nonn

AUTHOR

Chai Wah Wu, Mar 11 2022

STATUS

approved

editing