The On-Line Encyclopedia of Integer Sequences (OEIS)

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A355484

a(n) is the least positive number that can be represented in exactly n ways as 2*p+q where p and q are primes.
(history; published version)

#10 by Alois P. Heinz at Mon Jul 11 13:26:33 EDT 2022

STATUS

reviewed

approved

#9 by Michel Marcus at Mon Jul 11 12:52:16 EDT 2022

STATUS

proposed

reviewed

#8 by Robert Israel at Mon Jul 11 12:33:55 EDT 2022

STATUS

editing

proposed

#7 by Robert Israel at Mon Jul 11 12:33:46 EDT 2022

LINKS

Robert Israel, <a href="/A355484/b355484.txt">Table of n, a(n) for n = 0..2500</a>

MAPLE

L:= min(select(t -> V[t] = 0, [$1..K+1])):

STATUS

approved

editing

#6 by N. J. A. Sloane at Sun Jul 10 16:53:55 EDT 2022

STATUS

proposed

approved

#5 by Robert Israel at Sun Jul 03 23:29:55 EDT 2022

STATUS

editing

proposed

Discussion

Mon Jul 04

12:35

Hugo Pfoertner: Apart from the term "6": How does this differ from A335987?

Sun Jul 10

16:53

N. J. A. Sloane: I don't think we need both, and A355484 is more fundamental, so A335987 will be recycled

#4 by Robert Israel at Sun Jul 03 23:25:38 EDT 2022

CROSSREFS

Cf. A046926, A284052.

STATUS

proposed

editing

#3 by Robert Israel at Sun Jul 03 23:17:04 EDT 2022

STATUS

editing

proposed

#2 by Robert Israel at Sun Jul 03 23:09:29 EDT 2022

NAME

allocated for Robert Israela(n) is the least positive number that can be represented in exactly n ways as 2*p+q where p and q are primes.

DATA

1, 6, 9, 21, 17, 33, 45, 51, 75, 99, 111, 93, 105, 135, 153, 201, 165, 249, 231, 237, 321, 225, 273, 363, 411, 393, 285, 315, 471, 483, 435, 405, 465, 555, 681, 495, 783, 675, 873, 849, 963, 1729, 585, 525, 897, 795, 1041, 915, 735, 855, 1191, 825, 765, 1095, 975, 1005, 1035, 1125, 1311, 1407

OFFSET

0,2

COMMENTS

a(n) is the least number k such that A046926(k) = n.

EXAMPLE

a(3) = 21 because 21 can be written as 2*p+q with p and q prime in exactly 3 ways, namely 21 = 2*2+17 = 2*5+11 = 2*7+7, and no smaller number works.

MAPLE

M:= 3000: # to use primes up to M

P:= select(isprime, [2, seq(i, i=3..M, 2)]): nP:= nops(P):

A:= Vector(M):

for i from 1 do

p:= P[i];

if 2*p >= M then break fi;

for j from 1 to nP do

q:= P[j];

v:= 2*p+q;

if v > M then break fi;

A[v]:= A[v]+1;

od od:

K:= max(A):

V:= Array(0..K+1):

for i from 1 to M do

if V[A[i]] = 0 then V[A[i]]:= i fi

od:

L:= min(select(t -> V[t] = 0, [$1..K+1]):

convert(V[0..L-1], list);

CROSSREFS

Cf. A046926.

KEYWORD

allocated

nonn

AUTHOR

J. M. Bergot and Robert Israel, Jul 03 2022

STATUS

approved

editing

#1 by Robert Israel at Sun Jul 03 23:09:29 EDT 2022

NAME

allocated for Robert Israel

KEYWORD

allocated

STATUS

approved