A342837 - OEIS

%I #27 Mar 31 2021 22:27:34

%S 0,0,3,3,16,40,8,44,112,85,48,24,168,15,182,18,13,151,348,204,437,612,

%T 771,75,51,310,796,111,811,350,644,350,469,159,571,544,2239,4,1474,97,

%U 2177,175,1400,1791,75,1983,337,2503,854,2397,830,246,5350,1682,153,1581,622

%N 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).

%C The idea of this sequence comes from _Daniel Suteu_.

%C 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.

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

%F a(n) = primepi(A003618(n)) - primepi(A338968(n) mod 10^n). - _David A. Corneth_, Mar 29 2021

%e For a(2), as A338968(2) = A342834(2) = 7||97 = 797, a(2) = 0.

%e From _Daniel Suteu_, Mar 29 2021: (Start)

%e 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.

%e # 7||97||997 = 797997 = 3 * 17 * 15647 is not prime (#1 fail)

%e # 7||97||991 = 797991 = 3 * 461 * 577 is not prime (#2 fail)

%e # 7||97||983 = 797983 = 41 * 19463 is not prime (#3 fail)

%e # 7||97||977 = 797977 = A338968(3) is prime.

%e 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)

%Y Cf. A003618, A338968, A342834.

%K nonn,base

%O 1,3

%A _Bernard Schott_, Mar 29 2021

%E a(3)-a(57) from _Daniel Suteu_, Mar 29 2021