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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). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

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) = 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.

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

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)