

A342837


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


1



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
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OFFSET

1,3


COMMENTS

The idea of this sequence comes from Daniel Suteu.
A338968(n) is the concatenation of A342834(n1) with the largest ndigit prime p <= A003618(n) such that A342834(n1)p is prime where  stands for concatenation.
Both A338968(n) and A342834(n) have n*(n+1)/2 digits.


LINKS

Table of n, a(n) for n=1..57.


FORMULA

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


EXAMPLE

For a(2), as A338968(2) = A342834(2) = 797 = 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) = 797997 = 797997 while prime A338968(3) = 797977 = 797977.
# 797997 = 797997 = 3 * 17 * 15647 is not prime (#1 fail)
# 797991 = 797991 = 3 * 461 * 577 is not prime (#2 fail)
# 797983 = 797983 = 41 * 19463 is not prime (#3 fail)
# 797977 = 797977 = A338968(3) is prime.
Therefore, the largest 3digit prime p <= 997 such that A342834(2)p is prime, is p = 977. Through the sequence of the 3digit 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.
Sequence in context: A048234 A068415 A127539 * A278627 A231908 A226610
Adjacent sequences: A342834 A342835 A342836 * A342838 A342839 A342840


KEYWORD

nonn,base


AUTHOR

Bernard Schott, Mar 29 2021


EXTENSIONS

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


STATUS

approved



