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A171154 Smallest prime whose decimal expansion begins with concatenation of first n primes in descending order. 6
2, 3203, 5323, 75323, 11753221, 131175329, 171311753203, 19171311753229, 231917131175321, 292319171311753231, 3129231917131175327, 3731292319171311753239, 41373129231917131175321, 43413731292319171311753233, 4743413731292319171311753269, 534743413731292319171311753223 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence is conjectured to be infinite.
a(n) = "prime(n)...prime(1) R(n)".
R(n) for n>1: 03, 3, 3, 21, 9, 03, 29, 1, 31, 7, 39, 1, 33, 69, 23, 3, 59, 27, ...
It is conjectured that R(n)=1 for infinite many n.
REFERENCES
Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..298
EXAMPLE
a(1) = 2 = prime(1) is the exceptional case, because no R(1).
a(2) = 3203 = prime(453) = "32 03", R(2)="03".
a(5) = 11753221 = prime(772902) = "prime(5)...prime(1) 21", R(5)=21.
PROG
(Python)
from sympy import isprime, primerange, prime
def a(n):
if n == 1: return 2
c = int("".join(map(str, [p for p in primerange(2, prime(n)+1)][::-1])))
pow10 = 10
while True:
c *= 10
for b in range(1, pow10, 2):
if b%5 == 0: continue
if isprime(c+b):
return c+b
pow10 *= 10
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Mar 12 2022
CROSSREFS
Sequence in context: A358177 A175080 A243649 * A099689 A065671 A094211
KEYWORD
nonn,base
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 04 2009
EXTENSIONS
a(14) and beyond from Michael S. Branicky, Mar 12 2022
STATUS
approved

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Last modified April 21 13:26 EDT 2024. Contains 371870 sequences. (Running on oeis4.)