A091634
Number of primes less than 10^n which do not contain the digit 0.
Original entry on oeis.org
4, 25, 153, 1010, 7122, 52313, 397866, 3103348, 24649318, 198536215, 1616808581, 13287264748, 110033428309, 917072930187
Offset: 1
a(3) = 153 because there are 168 primes less than 10^3, 15 primes have at least one zero; 168 - 15 = 153.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 0] == {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
Table[PrimePi[10^n]-Total[Boole[DigitCount[#,10,0]>0]&/@ Prime[ Range[ PrimePi[ 10^n]]]],{n,8}] (* The program generates the first 8 terms of the sequence. To generate more, increase the digit 8 but the program may take a long time to run. *) (* Harvey P. Dale, Aug 26 2021 *)
-
from sympy import sieve # use primerange for larger terms
def nodigs0(n): return '0' not in str(n)
def aupton(terms):
ps, alst = 0, []
for n in range(1, terms+1):
ps += sum(nodigs0(p) for p in sieve.primerange(10**(n-1), 10**n))
alst.append(ps)
return alst
print(aupton(7)) # Michael S. Branicky, Apr 25 2021
A091646
Number of primes less than 10^n having at least one digit 2.
Original entry on oeis.org
1, 3, 29, 352, 3357, 32393, 312424, 3014171, 29016211, 279171099, 2685272908, 25829666453, 248507003625, 2391688694305
Offset: 1
a(2) = 3 because of the 25 primes less than 10^2, 3 have at least one digit 2.
A091647
Number of primes less than 10^n having at least one digit 3.
Original entry on oeis.org
1, 9, 66, 561, 4877, 43685, 399564, 3694303, 34433999, 322852288, 3041362298, 28758431735, 272777483044, 2594081699837
Offset: 1
a(2) = 9 because of the 25 primes less than 10^2, 9 have at least one digit 3.
-
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 3] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
A091707
Number of primes less than 10^n having at least one digit 6.
Original entry on oeis.org
0, 2, 32, 332, 3225, 31792, 309431, 2991216, 28863327, 278085918, 2677289604, 25769815303, 248050788931, 2388172543971
Offset: 1
a(1) = 0 because of the 4 primes less than 10^1, none have at least one digit 6.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 6] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
-
from sympy import sieve # use slower primerange for larger terms
def a(n): return sum('6' in str(p) for p in sieve.primerange(2, 10**n))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Apr 23 2021
A091708
Number of primes less than 10^n having at least one digit 7.
Original entry on oeis.org
1, 9, 68, 549, 4819, 43506, 397756, 3681943, 34344296, 322199867, 3036544958, 28722439343, 272501681533, 2591959274190
Offset: 1
a(1) = 1 because of the 4 primes less than 10^1, 1 has at least one digit 7.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 7] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
Table[Count[Prime[Range[PrimePi[10^n]]],?(DigitCount[#,10,7]>0&)],{n,12}] (* _Harvey P. Dale, Mar 03 2013 *)
A091709
Number of primes less than 10^n having at least one digit 8.
Original entry on oeis.org
0, 2, 27, 314, 3217, 31699, 308774, 2987107, 28824402, 277779084, 2674980022, 25752370493, 247919235555, 2387154761520
Offset: 1
a(2) = 2 because of the 25 primes less than 10^2, 2 have at least one digit 8.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 8] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
-
from sympy import sieve # use slower primerange for larger terms
def a(n): return sum('8' in str(p) for p in sieve.primerange(2, 10**n))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Apr 23 2021
A091710
Number of primes less than 10^n having at least one digit 9.
Original entry on oeis.org
0, 6, 60, 542, 4826, 43359, 397093, 3677641, 34316162, 321993007, 3035059323, 28710966351, 272413818120, 2591276923548
Offset: 1
a(2) = 6 because of the 25 primes less than 10^2, 6 have at least one digit 9.
-
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 9] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
A091705
Number of primes less than 10^n having at least one digit 4.
Original entry on oeis.org
0, 3, 32, 326, 3231, 31953, 310456, 3000349, 28922364, 278508004, 2680391313, 25793058269, 248228108241, 2389543008906
Offset: 1
a(2) = 3 because of the 25 primes less than 10^2, 3 have at least one digit 4.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 4] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
A091706
Number of primes less than 10^n having at least one digit 5.
Original entry on oeis.org
1, 3, 32, 324, 3282, 31949, 309669, 2995706, 28891689, 278270868, 2678674624, 25780340194, 248131741834, 2388797604792
Offset: 1
a(1) = 1 because of the 4 primes less than 10^1, 1 has at least one digit 5.
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = 1; Do[ While[ p = NextPrim[p]; p < 10^n, If[ Position[ IntegerDigits[p], 5] != {}, c++ ]]; Print[c]; p--, {n, 1, 8}] (* Robert G. Wilson v, Feb 02 2004 *)
Table[Count[Prime[Range[PrimePi[10^n]]],?(DigitCount[#,10,5]>0&)],{n,8}] (* _Harvey P. Dale, Dec 29 2012 *)
A373294
a(n) is the number of n-digit primes that have at least one zero among their digits (A056709).
Original entry on oeis.org
0, 0, 15, 204, 2251, 23715, 240528, 2391394, 23540109, 230318080, 2244729936, 21819401038, 211711461260, 2051836712085
Offset: 1
For n = 3, the 3-digit prime numbers that have the digit 0 are 101, 103, 107, 109, 307, 401, 409, 503, 509, 601, 607, 701, 709, 809 and 907. Therefore, a(3) = 15.
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a(n) = my(s=0); forprime(p=10^(n-1), 10^n-1, if (vecmin(digits(p)) == 0, s++)); s; \\ Michel Marcus, May 31 2024
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