A342837 Starting with A342834(n), a(n) is the number of n-digit primes we have to go back from A003618(n) through the sequence of these n-digit primes to get the prime A338968(n).

0, 0, 3, 3, 16, 40, 8, 44, 112, 85, 48, 24, 168, 15, 182, 18, 13, 151, 348, 204, 437, 612, 771, 75, 51, 310, 796, 111, 811, 350, 644, 350, 469, 159, 571, 544, 2239, 4, 1474, 97, 2177, 175, 1400, 1791, 75, 1983, 337, 2503, 854, 2397, 830, 246, 5350, 1682, 153, 1581, 622

Offset: 1

Author

Bernard Schott, Mar 29 2021

Keywords

• nonn
• base

Comments

The idea of this sequence comes from Daniel Suteu.

A338968(n) is the concatenation of A342834(n-1) with the largest n-digit prime p <= A003618(n) such that A342834(n-1)||p is prime where || stands for concatenation.

Both A338968(n) and A342834(n) have n*(n+1)/2 digits.

Examples

			For a(2), as A338968(2) = A342834(2) = 7||97 = 797, a(2) = 0.
From _Daniel Suteu_, Mar 29 2021: (Start)
For a(3), as A003618(1) = 7, A003618(2) = 97 and A003618(3) = 997, we have A342834(3) = 7||97||997 = 797997 while prime A338968(3) = 7||97||977 = 797977.
# 7||97||997 = 797997 = 3 * 17 * 15647 is not prime (#1 fail)
# 7||97||991 = 797991 = 3 * 461 * 577 is not prime (#2 fail)
# 7||97||983 = 797983 = 41 * 19463 is not prime (#3 fail)
# 7||97||977 = 797977 = A338968(3) is prime.
Therefore, the largest 3-digit prime p <= 997 such that A342834(2)||p is prime, is p = 977. Through the sequence of the 3-digit primes, we have to go back 3 primes from A003618(3) = 997 (991, 983, 977) in order to get A338968(3), hence a(3) = 3. (End)
		

Crossrefs

Cf. A003618, A338968, A342834.

Formula

a(n) = primepi(A003618(n)) - primepi(A338968(n) mod 10^n). - David A. Corneth, Mar 29 2021

Extensions

a(3)-a(57) from Daniel Suteu, Mar 29 2021