A136244 Least positive integer k such that 2k can be expressed as the sum of two primes in exactly n ways.

1, 2, 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, 540, 615, 759, 525, 570, 693, 645

Offset

0,2

Comments

It appears that 2, 3, 4, 6 are the only numbers k such that 2k can be expressed as the sum of two primes in only one way.

Except when n = 1, a(n) = A258713(n). The first 11 terms of this sequence are the same as the initial terms of A053033. If a(n) exists for all n then A053033 is a subsequence. - Andrew Howroyd, Jan 28 2020

Links

David A. Corneth, Table of n, a(n) for n = 0..16805 (first 1001 terms from Andrew Howroyd)

Index entries for sequences related to Goldbach conjecture

Formula

From Andrew Howroyd, Jan 28 2020: (Start)

a(n) = A023036(n) / 2.

A045917(a(n)) = n. (End)

Example

a(3) = 11: 22 = 3 + 19 = 5 + 17 = 11 + 11. Also 22 is the least number which could be expressed as the sum of two prime numbers in exactly three ways.

Prog

(PARI) a(n, lim=oo)={for(i=1, lim, my(s=0); forprime(p=2, i, s+=isprime(2*i-p)); if(s==n, return(i))); -1} \\ Andrew Howroyd, Jan 28 2020

Crossrefs

Cf. A023036, A045917, A053033, A126204, A258713.

Sequence in context: A220813 A217303 A053033 * A115057 A228344 A157421

Adjacent sequences: A136241 A136242 A136243 * A136245 A136246 A136247

Keyword

nonn

Author

K. B. Subramaniam (shunya_1950(AT)yahoo.co.in), Dec 24 2007

Extensions

a(0)=1 prepended, a(5) corrected and a(7) and beyond from Andrew Howroyd, Jan 28 2020

Status

approved