A339772 Number of Goldbach partitions of 2n whose parts have the same number of decimal digits.

0, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 3, 2, 2, 4, 2, 3, 5, 2, 3, 4, 1, 4, 5, 3, 3, 5, 3, 4, 7, 3, 3, 8, 3, 4, 6, 3, 5, 7, 3, 4, 6, 4, 4, 6, 3, 3, 7, 2, 2, 6, 2, 3, 4, 3, 2, 3, 3, 3, 3, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1

Offset

1,5

Links

Table of n, a(n) for n=1..93.

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..n} [floor(log_10(k)) = floor(log_10(2*n-k))] * c(k) * c(2*n-k), where [ ] is the Iverson bracket and c is the prime characteristic (A010051).

Example

a(7) = 1; 2*7 = 14 has two Goldbach partitions, (11,3) and (7,7). Since (7,7) is the only one whose parts have the same number of decimal digits, a(7) = 1.

Mathematica

Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]) KroneckerDelta[Floor[Log10[i]], Floor[Log10[2 n - i]]], {i, n}], {n, 100}]

Crossrefs

Cf. A010051, A055642.

Sequence in context: A093662 A284256 A354841 * A250211 A243753 A219238

Adjacent sequences: A339769 A339770 A339771 * A339773 A339774 A339775

Keyword

nonn,base

Author

Wesley Ivan Hurt, Dec 21 2020

Status

approved