A261806 a(n) = Sum from "least x such that prime(x) has n digits" to "the number of primes with n digits" of the difference between prime(k) and k.

7, 474, 42311, 3558614, 300169143, 25814402881, 2261786350515, 200839375217041, 18042305628036066, 1636922369808190765, 149754058084293423958, 13797718194530764325852, 1279006935910516590640721, 119184789951429474863414128, 11157358746329927416919291238, 1048709967153503078344158238498

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Lucas A. Brown, Python program.

Formula

a(n) = Sum_{k=A090226(n)..A006879(n)} prime(k)-k

Example

As 2, 3, 5, and 7 are the only primes less than 10, A006879(1) = 4 and as 1 is the least number such that prime(1) has 1 digit, A090226(1) = 1. Therefore a(1) = Sum_{k=1..4} prime(k)-k = (2-1) + (3-2) + (5-3) + (7-4) = 1 + 1 + 2 + 3 = 7.

Crossrefs

Cf. A006879, A014689, A090226.

Sequence in context: A112949 A254966 A345455 * A332147 A278143 A119621

Adjacent sequences: A261803 A261804 A261805 * A261807 A261808 A261809

Keyword

nonn,base

Author

Carauleanu Marc, Jul 09 2016

Extensions

a(7)-a(16) from Lucas A. Brown, Oct 21 2024

Status

approved