A185656
Final prime in first term of A019518 that is divisible by 7^n.
Original entry on oeis.org
11, 601, 601, 601, 107839, 577937, 8341631, 8341631, 8341631, 8341631, 8341631, 166778433637, 4054944029077, 58520914386689
Offset: 1
None of the numbers 2, 23, 235, and 2357 are divisible by 11, but 235711 is divisible by 7, so a(1)=11.
Not until the concatenation through 601 is such a number divisible by 7^2, so a(2)=601.
Cf.
A183194 and immediately following entries.
A185659
Final prime of first member of A019518 that is divisible by 11^n.
Original entry on oeis.org
17, 499, 13679, 221489, 712289, 7648813, 604578017, 7868766709
Offset: 1
2357111317 is divisible by 11, and concatenation through 499 is required for divisibility by 11^2.
A185662
Final prime of first member of A019518 that is divisible by 13^n.
Original entry on oeis.org
61, 149, 199, 349493, 5709623, 100776157, 1142774723
Offset: 1
The concatenations short of the one ending with 61 are not divisible by 13, while that one is.
A185665
Final prime of first member of A019518 that is divisible by 17^n.
Original entry on oeis.org
31, 1699, 1699, 901997, 24839599, 403445719, 2668745609
Offset: 1
235711131719232931 is divisible by 17.
A046035
Numbers k such that the concatenation of the first k primes (A019518) is a prime.
Original entry on oeis.org
1, 2, 4, 128, 174, 342, 435, 1429
Offset: 1
4 is a term since 2357 is a prime. [Corrected by Ed Murphy (emurphy42(AT)socal.rr.com), May 15 2007]
- R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that 719 is a term.]
Cf.
A033308 (Decimal expansion of Copeland-Erdős constant: concatenate primes).
-
max = 1500; With[{primes = Prime[Range[max]]}, Flatten[Position[ Table[ FromDigits[Flatten[IntegerDigits/@Take[primes, n]]], {n, max}], ?PrimeQ]]] (* _Harvey P. Dale, Dec 17 2013 *)
Position[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[Range[ 10^3]]]]], ?PrimeQ] // Flatten (* _Eric W. Weisstein, Oct 30 2015 *)
-
p=""; for(n=1, 2000, p=concat(p, prime(n)); if(ispseudoprime(eval(p)), print1(n", "))) \\ Altug Alkan, Oct 30 2015
A185671
Final prime of first member of A019518 that is divisible by 23^n.
Original entry on oeis.org
3, 5861, 58573, 3916021, 284728111, 1910245261
Offset: 1
While the very first concatenation is divisible by 23, 23^2 does not divide any such number until 5861 is adjoined.
A185677
Final prime adjoined in the smallest term of A019518 divisible by 31^n.
Original entry on oeis.org
107, 6619, 496897, 20005649, 308292781, 35800083049
Offset: 1
A183194
Final prime of first member of A019518 that is divisible by 3^n.
Original entry on oeis.org
29, 71, 71, 239, 239, 239, 13001, 50333, 50333, 374893, 1831913, 1831913, 3836171, 8467523, 8467523, 171374563, 2260865401, 2260865401, 2260865401, 2260865401, 2260865401, 1618263493747, 5212787222677, 5212787222677
Offset: 1
a(1)=29 since 2357111317192329 is divisible by 3.
a(22)-a(24) by Phil Carmody, Dec 29 2010
A185680
Final prime adjoined in the smallest term of A019518 divisible by 37^n.
Original entry on oeis.org
1051, 10037, 14029, 614659, 106458763, 78505687129
Offset: 1
A185704
Final prime adjoined in the smallest term of A019518 divisible by 73^n.
Original entry on oeis.org
593, 23909, 4851169, 84821071, 13231167673
Offset: 1
-
from sympy import nextprime
def A185704(n):
p, k, m = 2, 73**n, 10
q, m2 = p % k, m % k
while True:
p = nextprime(p)
while p >= m:
m *= 10
m2 = m % k
q = (q*m2 + p) % k
if q == 0:
return p # Chai Wah Wu, May 01 2020
Showing 1-10 of 84 results.
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