A073532
Number of n-digit primes with all digits distinct.
Original entry on oeis.org
4, 20, 97, 510, 2529, 10239, 33950, 90510, 145227, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
a(3)=97 because there are 97 three-digit primes with distinct digits: 103, 107, 109, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197,239, 241, 251, 257, 263, 269, 271, 281, 283, 293,307, 317, 347, 349, 359, 367, 379, 389, 397, 401, 409, 419, 421, 431, 439, 457, 461, 463, 467, 479, 487, 491, 503, 509, 521, 523, 541, 547, 563, 569, 571, 587, 593, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 673, 683, 691, 701, 709, 719, 739, 743, 751, 761, 769, 809, 821, 823, 827, 829, 839, 853, 857, 859, 863, 907, 937, 941, 947, 953, 967, 971, 983.
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lst = {}; Do[p = Prime@ n; If[ Union[Length /@ Split@ Sort@ IntegerDigits@ p] == {1}, AppendTo[lst, p]], {n, PrimePi[10^9]}]; Table[ Length@ Select[lst, 10^n < # < 10^(n + 1) &], {n, 0, 9}] (* Robert G. Wilson v, Jul 25 2008 *)
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from itertools import permutations
from sympy import isprime, primerange
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def a(n):
if n >= 10: return 0
return sum(isprime(int("".join(p))) for p in permutations("0123456789", n) if p[0] != '0')
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Apr 20 2021
A098224
Number of primes <=10^n in which decimal digits are all distinct.
Original entry on oeis.org
4, 24, 121, 631, 3160, 13399, 47349, 137859, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086, 283086
Offset: 1
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okQ[n_]:=Max[DigitCount[n]]==1
Table[Length[Select[Prime[Range[PrimePi[10^i]]],okQ]],{i,9}] (* Harvey P. Dale, Dec 12 2010 *)
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from sympy import sieve
def distinct_digs(n): s = str(n); return len(s) == len(set(s))
def aupton(terms):
ps, alst = 0, []
for n in range(1, terms+1):
if n >= 10: alst.append(ps); continue
ps += sum(distinct_digs(p) for p in sieve.primerange(10**(n-1), 10**n))
alst.append(ps)
return alst
print(aupton(35)) # Michael S. Branicky, Apr 24 2021
A098226
Number of primes <= 10^n which have repeated decimal digits.
Original entry on oeis.org
0, 1, 47, 598, 6432, 65099, 617230, 5623596, 50564448, 454769425, 4117771727, 37607628932, 346065253753, 3204941467716, 29844570139583, 279238340750839, 2623557157371147, 24739954287457774, 234057667276061521, 2220819602560635754, 21127269486018448842
Offset: 1
A099629
Smallest and largest primes pairwise displayed with k digits from k=1,...,9 with distinct decimal digits.
Original entry on oeis.org
2, 7, 13, 97, 103, 983, 1039, 9871, 10243, 98731, 102359, 987631, 1023467, 9876413, 10234589, 98765431, 102345689, 987654103
Offset: 1
A099630
Smallest and largest primes pairwise displayed with k digits from k=2,3,... with repeated decimal digits.
Original entry on oeis.org
11, 11, 101, 997, 1009, 9973, 10007, 99991, 100003, 999983, 1000003, 9999991, 10000019, 99999989, 100000007, 999999937, 1000000007, 9999999967, 10000000019, 99999999977, 100000000003, 999999999989, 1000000000039, 9999999999971, 10000000000037, 99999999999973
Offset: 1
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Join[{11,11},Flatten[Table[{NextPrime[10^n],NextPrime[10^(n+1),-1]}, {n,2,20}]]] (* Harvey P. Dale, Jun 04 2018 *)
Showing 1-5 of 5 results.
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