A176942
Champernowne primes.
Original entry on oeis.org
1234567891, 12345678910111, 123456789101112131415161
Offset: 1
- R. W. Stephan, Factors and primes in two Smarandache sequences.
Cf.
A007376 (infinite Barbier word = almost-natural numbers: write n in base 10 and juxtapose digits).
Cf.
A033307 (decimal expansion of Champernowne constant).
Cf.
A071620 (number of digits in the n-th Champernowne prime).
See
A265043 for where to end the string of numbers that are being concatenated in order to get the n-th prime.
-
With[{no=500},FromDigits/@Select[Table[Take[Flatten[IntegerDigits/@Range[no]],n],{n,no}],PrimeQ[FromDigits[#]]&]] (* Harvey P. Dale, Feb 06 2011 *)
Select[Table[Floor[N[ChampernowneNumber[10], n]*10^n], {n, 24}], PrimeQ] (* Arkadiusz Wesolowski, May 10 2012 *)
A171154
Smallest prime whose decimal expansion begins with concatenation of first n primes in descending order.
Original entry on oeis.org
2, 3203, 5323, 75323, 11753221, 131175329, 171311753203, 19171311753229, 231917131175321, 292319171311753231, 3129231917131175327, 3731292319171311753239, 41373129231917131175321, 43413731292319171311753233, 4743413731292319171311753269, 534743413731292319171311753223
Offset: 1
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 04 2009
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.
- Leonard E. Dickson, History of the Theory of numbers, vol. I, Dover Publications 2005.
-
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
A108471
Smallest prime with a run of n strictly increasing digits.
Original entry on oeis.org
2, 13, 127, 1237, 12347, 123457, 1234789, 12356789, 1234567891, 100123456789
Offset: 1
A178928
Smallest semiprime containing leading sequence of n ascending numbers.
Original entry on oeis.org
10, 121, 123, 1234, 123451, 1234561, 1234567, 123456782, 12345678911, 123456789101, 123456789101117, 12345678910111229, 123456789101112133, 123456789101112131414, 1234567891011121314159
Offset: 1
a(1) = 10 because 10 = 2 * 5 is the smallest semiprime (or biprime, products of two primes) whose leftmost (base 10) digit is 1.
a(2) = 121 because 121 = 11^2 semiprime whose leftmost digits are 12.
a(3) = 123 since it is a semiprime already.
a(4) = 1234 = 2 * 617.
a(5) = 123451 = 41 * 3011.
a(6) = 1234561 = 211 * 5851.
-
semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 0, m = FromDigits@ Flatten@ IntegerDigits@ Range@ n}, If[ semiPrimeQ@ m, , While[a = 10^(1 + Max[0, Floor@ Log10@ k]) m + k; ! semiPrimeQ@ a, k++]; m = a]; m]; Array[f, 15]
Showing 1-4 of 4 results.
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