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
A098227
Number of primes with exactly n decimal digits which have repeated digits.
Original entry on oeis.org
0, 1, 46, 551, 5834, 58667, 552131, 5006366, 44940852, 404204977, 3663002302, 33489857205, 308457624821, 2858876213963, 26639628671867, 249393770611256, 2344318816620308, 22116397130086627, 209317712988603747
Offset: 1
Above n = 9 a(n) = A006879(n) because above 10 there must be a repetition. At n = 10 the sum of digits 0+1+2+3+4+5+6+7+8+9=45 is divisible by 3, so no primes with 10 distinct decimal digits exist.
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Table[Count[Prime@ Range[If[# == 0, 1, # + 1] &@ PrimePi[10^n], PrimePi[10^(n + 1) - 1]], p_ /; Total@ Boole@ Map[# > 1 &, DigitCount@ p] > 0], {n, 0, 6}] (* Michael De Vlieger, Mar 26 2017 *)
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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