A001172 -id:A001172 - cp's OEIS frontend

A258713 A001172(n)/2: Least k such that 2k is a sum of two odd primes in exactly n ways.

0, 3, 5, 11, 17, 24, 30, 39, 42, 45, 57, 72, 60, 84, 90, 117, 123, 144, 120, 105, 162, 150, 180, 237, 165, 264, 288, 195, 231, 240, 210, 285, 255, 336, 396, 378, 438, 357, 399, 345, 519, 315, 504, 465, 390, 480, 435, 462, 450, 567, 717, 420, 495, 651

Offset: 0

N. J. A. Sloane, Jun 14 2015

nonn

Up to a(14) also indices of records in A002375, number of ways to write 2n as sum of two odd primes. - M. F. Hasler, Aug 21 2017

Robert Israel, Table of n, a(n) for n = 0..845

Cf. A136244, A001172.

Cf. A002375, A002372, A045917.

g:= add(x^ithprime(i),i=2..1000):
G:= series((g^2+add(x^(2*ithprime(i)),i=2..1000))/2,x,ithprime(1001)+3):
A[0]:= 0:
for k from 1 to (ithprime(1001)+1)/2 do
  m:= coeff(G,x,2*k);
  if not assigned(A[m]) then A[m]:= k fi;
od:
for m from 1 while assigned(A[m]) do od:
seq(A[i],i=0..m-1); # Robert Israel, Aug 21 2017

With[{s = Array[Count[Select[IntegerPartitions[2 #, 2], Length@ # == 2 &], p_ /; AllTrue[p, And[PrimeQ@ #, OddQ@ #] &]] &, 10^3]}, Table[FirstPosition[s, n][[1]] /. 1 -> 0, {n, 0, 53}]] (* Michael De Vlieger, Aug 21 2017 *)

Edited by M. F. Hasler, Aug 21 2017

Edited by Robert Israel, Aug 21 2017

A000666 Number of symmetric relations on n nodes.

Original entry on oeis.org

1, 2, 6, 20, 90, 544, 5096, 79264, 2208612, 113743760, 10926227136, 1956363435360, 652335084592096, 405402273420996800, 470568642161119963904, 1023063423471189431054720, 4178849203082023236058229792, 32168008290073542372004082199424

Offset: 0

N. J. A. Sloane

Each node may or may not be related to itself.
Also the number of rooted graphs on n+1 nodes.
The 1-to-1 correspondence is as follows: Given a rooted graph on n+1 nodes, replace each edge joining the root node to another node with a self-loop at that node and erase the root node. The result is an undirected graph on n nodes which is the graph of the symmetric relation.
Also the number of the graphs with n nodes whereby each node is colored or not colored. A loop can be interpreted as a colored node. - Juergen Will, Oct 31 2011

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, pp. 101, 241.
M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

David Applegate, Table of n, a(n) for n = 0..80 [Shortened file because terms grow rapidly: see Applegate link below for additional terms]
David Applegate, Table of n, a(n) for n = 0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
R. L. Davis, The number of structures of finite relations, Proc. Amer. Math. Soc. 4 (1953), 486-495.
R. L. Davis, Structure of dominance relations, Bull. Math. Biophys., 16 (1954), 131-140. [Annotated scanned copy]
F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Am. Math. Soc. 78 (1955) 445-463, eq. (24).
Frank Harary, Edgar M. Palmer, Robert W. Robinson and Allen J. Schwenk, Enumeration of graphs with signed points and lines, J. Graph Theory 1 (1977), no. 4, 295-308.
Adib Hassan, Po-Chien Chung and Wayne B. Hayes, Graphettes: Constant-time determination of graphlet and orbit identity including (possibly disconnected) graphlets up to size 8, arXiv:1708.04341 [cs.DS], 2017.
Mathematics Stack Exchange, Enumerating Graphs with Self-Loops, Jan 23 2014.
M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sep. 15, 1955, pp. 14-22. [Annotated scanned copy]
W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
W. Oberschelp, The number of non-isomorphic m-graphs, Presented at Mathematical Institute Oberwolfach, July 3 1967 [Scanned copy of manuscript]
W. Oberschelp, Strukturzahlen in endlichen Relationssystemen, in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968. [Annotated scanned copy]
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
Marko Riedel, Maple code for sequence.
Marko Riedel et al., Enumerating Graphs with Self-Loops
R. W. Robinson, Notes - "A Present for Neil Sloane"
R. W. Robinson, Notes - computer printout
Sage, Common Graphs (Graph Generators)
Lorenzo Sauras-Altuzarra, Graphs
J. M. Tangen and N. J. A. Sloane, Correspondence, 1976-1976
Eric Weisstein's World of Mathematics, Rooted Graph

Cf. A000595, A001172, A001174, A006905, A000250, A054921 (connected relations).

Maple
```
# see Riedel link above
```

Join[{1,2}, Table[CycleIndex[Join[PairGroup[SymmetricGroup[n]], Permutations[Range[n*(n-1)/2+1, n*(n+1)/2]], 2],s] /. Table[s[i]->2, {i,1,n^2-n}], {n,2,8}]] (* Geoffrey Critzer, Nov 04 2011 *)
Table[Module[{eds,pms,leq},
eds=Select[Tuples[Range[n],2],OrderedQ];
pms=Map[Sort,eds/.Table[i->Part[#,i],{i,n}]]&/@Permutations[Range[n]];
leq=Function[seq,PermutationCycles[Ordering[seq],Length]]/@pms;
Total[Thread[Power[2,leq]]]/n!
],{n,0,8}] (* This is after Geoffrey Critzer's program but does not use the (deprecated) Combinatorica package. - Gus Wiseman, Jul 21 2016 *)
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
edges[v_] := Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i-1}], {i, 2, Length[v]}] + Sum[Quotient[v[[i]], 2] + 1, {i, 1, Length[v]}];
a[n_] := a[n] = (s = 0; Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/n!);
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 17}] (* Jean-François Alcover, Nov 13 2017, after Andrew Howroyd *)

permcount(v) = {my(m=1,s=0,k=0,t); for(i=1,#v,t=v[i]; k=if(i>1&&t==v[i-1],k+1,1); m*=t*k;s+=t); s!/m}
edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i],v[j]))) + sum(i=1, #v, v[i]\2 + 1)}
a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*2^edges(p)); s/n!} \\ Andrew Howroyd, Oct 22 2017

from itertools import combinations
from math import prod, factorial, gcd
from fractions import Fraction
from sympy.utilities.iterables import partitions
def A000666(n): return int(sum(Fraction(1<>1)+1)*r+(q*r*(r-1)>>1) for q, r in p.items()),prod(q**r*factorial(r) for q, r in p.items())) for p in partitions(n))) # Chai Wah Wu, Jul 02 2024

Euler transform of A054921. - N. J. A. Sloane, Oct 25 2018
Let G_{n+1,k} be the number of rooted graphs on n+1 nodes with k edges and let G_{n+1}(x) = Sum_{k=0..n(n+1)/2} G_{n+1,k} x^k. Thus a(n) = G_{n+1}(1). Let S_n(x_1, ..., x_n) denote the cycle index for Sym_n. (cf. the link in A000142).
Compute x_1*S_n and regard it as the cycle index of a set of permutations on n+1 points and find the corresponding cycle index for the action on the n(n+1)/2 edges joining those points (the corresponding "pair group"). Finally, by replacing each x_i by 1+x^i gives G_{n+1}(x). [Harary]
Example, n=2. S_2 = (1/2)*(x_1^2+x_2), x_1*S_2 = (1/2)*(x_1^3+x_1*x_2). The pair group is (1/2)*(x_1^2+x_1*x_2) and so G_3(x) = (1/2)*((1+x)^3+(1+x)*(1+x^2)) = 1+2*x+2*x^2+x^3; set x=1 to get a(2) = 6.
a(n) ~ 2^(n*(n+1)/2)/n! [McIlroy, 1955]. - Vaclav Kotesovec, Dec 19 2016

Description corrected by Christian G. Bower
More terms from Vladeta Jovovic, Apr 18 2000
Entry revised by N. J. A. Sloane, Mar 06 2007

A023036 Smallest positive even integer that is an unordered sum of two primes in exactly n ways.

Original entry on oeis.org

2, 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, 1080

Offset: 0

David W. Wilson, Jun 14 1998

Except for first two terms, same as A001172.
The first occurrence of k in A045917.
The graph looks like a comet. - Daniel Forgues, Jun 12 2014

			a(3) = 22 as 22 = (19+3) = (17+5) = (11+11). There are exactly 3 ways 22 can be expressed as the sum of two primes and no even number less than 22 can be so expressed.
From _Daniel Forgues_, Jun 13 2014: (Start)
Terms for n = 1..6 and corresponding sums:
  a(1) =  4 =  2 + 2;
  a(2) = 10 =  7 + 3 =  5 +  5;
  a(3) = 22 = 19 + 3 = 17 +  5 = 11 + 11;
  a(4) = 34 = 31 + 3 = 29 +  5 = 23 + 11 = 17 + 17;
  a(5) = 48 = 43 + 5 = 41 +  7 = 37 + 11 = 31 + 17 = 29 + 19;
  a(6) = 60 = 53 + 7 = 47 + 13 = 43 + 17 = 41 + 19 = 37 + 23 = 31 + 29.
(End)

Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)
Index entries for sequences related to Goldbach conjecture

Cf. A045917, A000954, A136244, A258713.

f[n_] := Length@ Select[2n - Prime@ Range@ PrimePi@ n, PrimeQ]; nn = 100; t = Table[0, {nn}]; k = 1; cnt = 0; While[cnt < nn, a = f@k; If[a <= nn && t[[a]] == 0, t[[a]] = 2 k; cnt++]; k++]; t (* Robert G. Wilson v, Mar 15 2011 *)

A000954 Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.

Original entry on oeis.org

2, 12, 68, 128, 152, 188, 332, 398, 368, 488, 632, 692, 626, 992, 878, 908, 1112, 998, 1412, 1202, 1448, 1718, 1532, 1604, 1682, 2048, 2252, 2078, 2672, 2642, 2456, 2936, 2504, 2588, 2978, 3092, 3032, 3218, 3272, 3296, 3632, 3548, 3754, 4022, 4058, 4412

Offset: 0

Bill Gosper

The Goldbach conjecture is that every even number is the sum of two primes.

			2 is largest even integer which is the sum of two primes in 0 ways, 12 is largest even integer which is the unordered sum of two primes in 1 way (5+7), etc.

T. D. Noe, Table of n, a(n) for n = 0..5000

Cf. A045917, A023036, A000974, A001172, A002375.

f[n_] := Block[{c = 0, k = 3}, While[k <= n/2, If[PrimeQ[k] && PrimeQ[n - k], c++ ]; k++ ]; c]; a = Table[0, {50}]; a[[1]] = 2; a[[2]] = 4; Do[m = n; b = f[n]; If[b < 100, a[[b + 1]] = n], {n, 6, 20000, 2}] (* Robert G. Wilson v, Dec 20 2003 *)

A025018 Numbers k such that least prime in the Goldbach partition of k increases.

Original entry on oeis.org

4, 6, 12, 30, 98, 220, 308, 556, 992, 2642, 5372, 7426, 43532, 54244, 63274, 113672, 128168, 194428, 194470, 413572, 503222, 1077422, 3526958, 3807404, 10759922, 24106882, 27789878, 37998938, 60119912, 113632822, 187852862, 335070838

Offset: 1

David W. Wilson

Charles R Greathouse IV, Table of n, a(n) for n = 1..69 (from Tomás Oliveira e Silva)
Mark A. Herkommer, Goldbach Conjecture Research
Jorg Richstein, Verifying Goldbach's Conjecture up to 4 * 10^14, Math. of Computation, Vol. 70, No. 236, pp. 1745-1749 (July 2000)
Index entries for sequences related to Goldbach conjecture
Tomás Oliveira e Silva, Goldbach conjecture verification

Cf. A001172, A025019.

p = 1; r = {}; Do[ k = 2; While[ !PrimeQ[k] || !PrimeQ[2n - k], k++ ]; If[k > p, p = k; r = Append[r, 2n]], {n, 2, 10^8}]; r

Gold(n)=forprime(p=2,min(n\2,default(primelimit)),if(isprime(n-p),return(p)))
r=0;forstep(n=4,1e6,2,t=Gold(n);if(t>r,r=t;print1(n", "))) \\ Charles R Greathouse IV, Feb 21 2012

Edited and extended by Robert G. Wilson v, Dec 13 2002

A103152 Smallest odd number which can be written as a sum 2p+q (where p and q are both odd primes, A065091) in exactly n ways, zero if there are no such odd number.

Original entry on oeis.org

9, 13, 17, 29, 45, 51, 69, 81, 99, 93, 105, 135, 153, 201, 195, 165, 231, 237, 321, 297, 225, 363, 725, 393, 285, 315, 471, 483, 435, 405, 465, 561, 555, 495, 609, 783, 675, 867, 849, 963, 645, 525, 693, 897, 795, 915, 987, 735, 855, 825, 765, 1095, 975, 1467

Offset: 1

Lei Zhou, Feb 09 2005

nonn

Conjecture: except for the 2nd, 3rd and 4th terms, all other terms are divisible by 3; See also comments in A103151.
a(23)=725 is also not divisible by 3. [D. S. McNeil, Sep 06 2010]
The only terms a(n) not divisible by 3 for n <= 1450 are a(2),a(3),a(4) and a(23). - Robert Israel, Mar 17 2020

			9 is the smallest odd number with just one such composition: 9 = 3+2*3, thus a(1)=9.
Similarly, 13 is smallest with exactly 2 compositions: 13 = 3+2*5 = 7+2*3, thus a(2)=13.

Robert Israel, Table of n, a(n) for n = 1..1450

Cf. A103151, A001172, A001031.

N:= 2000: # for terms before the first term > N
P:= select(isprime, [seq(i,i=3..N,2)]):
nP:= nops(P):
V:= Vector(N):
for i from 1 while 2*P[i] N then break fi;
    V[k]:= V[k]+1;
od od:
A:= Vector(N):
for i from 1 to N by 2 do if V[i] <> 0 and A[V[i]] = 0 then A[V[i]]:= i fi od:
for i from 1 to N do if A[i] = 0 then break fi od:
seq(A[j],j=1..i-1); # Robert Israel, Mar 17 2020

Array[a, 300]; Do[a[n] = 0, {n, 1, 300}]; n = 9; ct = 0; While[ct < 200, m = 3; ct = 0; While[(m*2) < n, If[PrimeQ[m], cp = n - (2* m); If[PrimeQ[cp], ct = ct + 1]]; m = m + 2]; If[a[ct] == 0, a[ct] = n]; n = n + 2]; Print[a]

(define (A103152 n) (+ 1 (* 2 (first-n-where-fun_n-is-i1 A103151 n))))
(define (first-n-where-fun_n-is-i1 fun i) (let loop ((n 1)) (cond ((= i (fun n)) n) (else (loop (+ n 1)))))) ;; Antti Karttunen, Jun 19 2007

Starting offset changed from 0 to 1 by Antti Karttunen, Jun 19 2007

A000974 Conjecturally the number of even integers the sum of two primes in exactly n ways.

Original entry on oeis.org

1, 4, 9, 11, 11, 16, 16, 18, 20, 23, 16, 29, 16, 25, 27, 23, 22, 25, 35, 29, 26, 25, 27, 27, 27, 33, 28, 44, 35, 21, 29, 35, 38, 33, 39, 37, 34, 35, 31, 31, 28, 41, 37, 32, 44, 35, 37, 41, 44, 33, 37, 32, 47, 39, 43, 47, 33, 37, 48, 41, 37, 48, 34, 35, 47, 36, 29, 36, 46, 44, 43, 38, 48

Offset: 0

Bill Gosper

nonn

T. D. Noe, Table of n, a(n) for n = 0..5000

Cf. A000954, A001172, A002375.

f[n_] := Length[ Select[2n - Prime[ Range[ PrimePi[n]]], PrimeQ]]; a = Table[0, {75}]; Do[c = f[n]; If[c < 75, a[[c + 1]]++ ], {n, 5000}]; a (* Robert G. Wilson v, using Paul Abbott's coding in A002375, Apr 07 2005 *)

A082917 Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number.

Original entry on oeis.org

6, 10, 22, 34, 48, 60, 78, 84, 90, 114, 120, 168, 180, 210, 300, 330, 390, 420, 510, 630, 780, 840, 990, 1050, 1140, 1260, 1470, 1650, 1680, 1890, 2100, 2310, 2730, 3150, 3570, 3990, 4200, 4410, 4620, 5250, 5460, 6090, 6510, 6930, 7980, 8190, 9030, 9240

Offset: 1

Hugo Pfoertner, Apr 15 2003

nonn

The terms up to 114 are identical with A001172. The record-setting number of decompositions is given by A082918.

It appears that every primorial number (A002110) greater than 30 is in this sequence. Sequence A116979 gives the number of decompositions for n equal to a primorial number. - T. D. Noe, Mar 15 2010

			a(1) = 6 = 3 + 3.
a(2) = 10 because 10 is the smallest number that can be written in two ways: 10 = 3 + 7 = 5 + 5.

Bill Hannaford, Table of n, a(n) for n = 1..420 (first 244 terms from T. D. Noe)

Cf. A002375, A001172, A082918. A109679 is another version of the same sequence.

kmax = 40000;
ip[k_] := IntegerPartitions[k, {2}, Select[Range[3, k-1], PrimeQ]];
seq = Module[{k, lg, record = 0, n = 0}, Reap[For[k = 6, k <= kmax, k = k+2, lg = Length[ip[k]]; If[lg > record, record = lg; n = n+1; Print["a(", n, ") = ", k]; Sow[k]]]][[2, 1]]] (* Jean-François Alcover, Jun 04 2022 *)

A105093 Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k.

Original entry on oeis.org

18, 24, 30, 36, 60, 84, 120, 162, 204, 210, 216, 240, 288, 330, 372, 390, 456, 520, 540, 624, 726, 762, 798, 840, 852, 882, 924, 978, 990, 1104, 1140, 1164, 1200, 1392, 1410, 1428, 1530, 1632, 1650, 1716, 1740, 1764, 1794, 1848, 1974, 2052, 2100, 2112, 2184

Offset: 1

Giovanni Teofilatto, Apr 06 2005

nonn

			a(1)=18 because prime(3)+prime(6)=prime(4)+prime(5)=5+13=7+11=18.

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Goldbach Conjecture

Cf. A001172, A000954, first primes in A022885.

lst = {}; Do[ If[ Prime[n] + Prime[n + 3] == Prime[n + 1] + Prime[n + 2], AppendTo[lst, Prime[n] + Prime[n + 3]]], {n, 184}]; lst (* Robert G. Wilson v, Apr 07 2005 *)

from sympy import nextprime
A105093_list, plist = [], [2,3,5,7]
while len(A105093_list) < 10000:
    m = plist[0]+plist[3]
    if m == plist[1]+plist[2]:
        A105093_list.append(m)
    plist = plist[1:] + [nextprime(plist[-1])] # Chai Wah Wu, Mar 30 2020

Edited and extended by Robert G. Wilson v, Apr 07 2005

A280867 Least k such that k is the sum of two totient numbers (A002202) in exactly n ways, or 0 if no such k exists.

Original entry on oeis.org

2, 8, 12, 20, 24, 32, 40, 50, 48, 62, 60, 64, 76, 102, 88, 108, 120, 128, 112, 136, 152, 148, 186, 168, 180, 192, 184, 216, 252, 236, 208, 220, 244, 232, 308, 268, 280, 292, 336, 304, 368, 328, 384, 364, 352, 408, 440, 376, 432, 400, 436, 388, 448, 492, 460, 484, 472, 548

Offset: 1

Altug Alkan, Jan 28 2017

nonn

Least k such that A281687(k/2) = n, or 0 if no such k exists.

See also graph of A001172 for similar points.

			a(4) = 20 because 20 = 2 + 18 = 4 + 16 = 8 + 12 = 10 + 10; 2, 4, 8, 10, 12, 16, 18 are in A002202 and 20 is the least number with this property.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A000010, A001172, A002202, A281687.

a281687(n) = sum(k=1, n, istotient(k) && istotient(2*n-k));
a(n) = my(k=1); while(a281687(k) != n, k++); 2*k;

do(n)=my(u=select(istotient, [1..n]),v=vector(n),t); for(i=1,#u, for(j=i,#u, t=u[i]+u[j]; if(t>n, break); v[t]++)); t=vector(vecmax(v)); for(i=1,#v, if(v[i] && t[v[i]]==0, t[v[i]]=i)); for(i=1,#t, if(t[i]==0, return(t[1..i-1]))); t \\ Charles R Greathouse IV, Jan 29 2017

cp's OEIS Frontend

A258713 A001172(n)/2: Least k such that 2k is a sum of two odd primes in exactly n ways.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A000666 Number of symmetric relations on n nodes.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

Extensions

A023036 Smallest positive even integer that is an unordered sum of two primes in exactly n ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A000954 Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A025018 Numbers k such that least prime in the Goldbach partition of k increases.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A103152 Smallest odd number which can be written as a sum 2p+q (where p and q are both odd primes, A065091) in exactly n ways, zero if there are no such odd number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Scheme

Extensions

A000974 Conjecturally the number of even integers the sum of two primes in exactly n ways.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A082917 Numbers that can be expressed as the sum of two odd primes in more ways than any smaller even number.

Views