A340063 -id:A340063 - cp's OEIS frontend

A340294 a(n) = pi(A340063(n)) = A000720(A340063(n)) for prime A340063(n) and otherwise k such that A340063 is the k-th positive integer having its digitsum.

1, 1, 2, 2, 3, 3, 3, 4, 1, 5, 5, 6, 2, 4, 7, 6, 8, 3, 5, 9, 1, 10, 7, 11, 2, 6, 12, 3, 13, 8, 14, 4, 7, 15, 2, 16, 3, 17, 9, 18, 4, 8, 19, 5, 20, 10, 21, 4, 22, 5, 9, 23, 5, 24, 1, 25, 6, 10, 26, 11, 27, 7, 28, 12, 29, 7, 11, 30, 1, 6, 31, 8, 32, 6, 33, 13, 34, 2

Offset: 1

David A. Corneth, Jan 03 2021

			a(17) = 8 as A340063(17) = 19 which is the 8th prime.
a(25) = 2 as A340063(25) = 14 which is composite and 14 is the second positive integer with digitsum 5.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A000720, A254524, A340063.

A340202 Primes followed by the difference from the next prime calculated by adding the digits of the lexicographically earliest distinct term.

Original entry on oeis.org

2, 1, 3, 20, 5, 110, 7, 4, 11, 200, 13, 22, 17, 1001, 19, 40, 23, 6, 29, 1010, 31, 15, 37, 112, 41, 1100, 43, 121, 47, 24, 53, 33, 59, 2000, 61, 42, 67, 130, 71, 10001, 73, 51, 79, 202, 83, 60, 89, 8, 97, 220, 101, 10010, 103, 301, 107, 10100, 109, 310, 113

Offset: 1

Carole Dubois, Dec 31 2020

			Prime 2 + (1) = prime 3;
prime 3 + (2+0) = prime 5;
prime 5 + (1+1+0) = prime 7;
prime 7 + (4) = prime 11;
prime 11 + (2+0+0) = prime 13;
prime 13 + (2+2) = 17; etc.

Cf. A000040 (primes), A219606.

Differences between consecutive primes: A001223, A134735, A340063.

cp's OEIS Frontend

A340294 a(n) = pi(A340063(n)) = A000720(A340063(n)) for prime A340063(n) and otherwise k such that A340063 is the k-th positive integer having its digitsum.

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