A090226 -id:A090226 - cp's OEIS frontend

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

Carauleanu Marc, Jul 09 2016

			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.

Lucas A. Brown, Python program.

Cf. A006879, A014689, A090226.

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

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

A164054 The index values of the smallest and the largest n-digit primes.

Original entry on oeis.org

1, 4, 5, 25, 26, 168, 169, 1229, 1230, 9592, 9593, 78498, 78499, 664579, 664580, 5761455, 5761456, 50847534, 50847535, 455052511, 455052512, 4118054813, 4118054814, 37607912018, 37607912019, 346065536839, 346065536840, 3204941750802, 3204941750803, 29844570422669, 29844570422670

Offset: 1

Parthasarathy Nambi, Aug 08 2009

Union of A006880 (except 0) and A090226. - Parthasarathy Nambi, Sep 19 2009

			The index value of the smallest six digit prime number is 9593. The index value of the largest six digit prime number is 78498.

Cf. A000040, A006880, A090226.

More terms from Amiram Eldar, Nov 30 2019

A300186 Largest digit sum among all n-digit primes.

Original entry on oeis.org

7, 17, 25, 35, 44, 53, 62, 71, 80, 88, 98, 107, 115, 125, 134, 143, 152, 161, 170, 179, 188, 197, 206, 215, 223, 233, 242, 250, 260, 269, 278, 287, 296, 304, 314, 323, 332, 341, 350, 359, 367, 377, 386, 394, 404, 413, 421, 431, 440, 449, 458, 466, 476, 485, 494

Offset: 1

Felix Fröhlich, Feb 28 2018

Largest value of A007605(x) for any integer x in the interval [A090226(n), A090226(n+1)-1].

Trivially, 1 < a(n) < 9*n = A008591(n). The lower bound follows, since a prime > 10 must contain at least two nonzero digits, with the least possible digit sum 2. The upper bound follows because 10^n-1 is always composite and thus the digit sum can be at most A017257(n-1). The maximal possible value is reached by a(n) iff a term t exists in A263431 such that A055642(t) = n-1.

			For n = 2: Among all 2-digit primes, the largest possible digit sum is 8+9 = 17, which is achieved by the prime 89, so a(2) = 17.

Cf. A007605, A008591, A017257, A055642, A090226, A263431.

a(n) = my(r=0); forprime(p=10^(n-1), 10^n, if(sumdigits(p) > r, r=sumdigits(p))); r

More terms from Alois P. Heinz, Feb 28 2018

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

Extensions

A164054 The index values of the smallest and the largest n-digit primes.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A300186 Largest digit sum among all n-digit primes.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions