A352296 - OEIS

A352296

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

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

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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)

LINKS

Table of n, a(n) for n=0..53.

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 *)

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.

Essentially the same as A023036 and A001172.

Sequence in context: A235142 A250398 A112774 * A369385 A227225 A008178

Adjacent sequences: A352293 A352294 A352295 * A352297 A352298 A352299

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Mar 11 2022

STATUS

approved