A119297
Total number of 6's digits in the first 10^n primes.
Original entry on oeis.org
0, 10, 315, 3824, 47269, 560677, 7079879, 79433407, 887292243, 9778050835, 110518283071, 1198946387631
Offset: 1
At a(2)=10 there are 10 6's digits in the first 10^2 primes.
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A119297 := proc(n) option remember: local k,s,lim: if(n=0)then return 0:fi: lim:=10^n: s:=procname(n-1): for k from 10^(n-1)+1 to lim do s:=s+nops([SearchAll("6",convert(ithprime(k),string))]): od: return s: end: seq(A119297(n),n=1..4); # Nathaniel Johnston, May 09 2011
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Table[Count[IntegerDigits[Prime[Range[10^n]]], 6, 2], {n, 6}] (* Robert Price, May 02 2019 *)
A119298
Total number of 7's digits in the first 10^n primes.
Original entry on oeis.org
2, 34, 551, 6338, 72319, 809360, 9543704, 104376285, 1136782466, 12273965395, 134080968533, 1448607569210
Offset: 1
At a(1)=2 there are 2 7's digits in the first 10^1 primes.
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A119298 := proc(n) option remember: local k,s,lim: if(n=0)then return 0:fi: lim:=10^n: s:=procname(n-1): for k from 10^(n-1)+1 to lim do s:=s+nops([SearchAll("7",convert(ithprime(k),string))]): od: return s: end: seq(A119298(n),n=1..4); # Nathaniel Johnston, May 09 2011
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Table[Count[IntegerDigits[Prime[Range[10^n]]], 7, 2], {n, 6}] (* Robert Price, May 02 2019 *)
Table[Total[Table[DigitCount[p,10,7],{p,Prime[Range[10^n]]}]],{n,7}] (* The program generates the first seven terms of the sequence. *) (* Harvey P. Dale, Dec 10 2024 *)
A268839
a(n) = Sum_{j=1..10^n-1} 2^f(j) where f(j) is the number of zero digits in the decimal representation of j.
Original entry on oeis.org
9, 108, 1197, 13176, 144945, 1594404, 17538453, 192922992, 2122152921, 23343682140, 256780503549, 2824585539048, 31070440929537, 341774850224916, 3759523352474085, 41354756877214944, 454902325649364393, 5003925582143008332, 55043181403573091661
Offset: 1
a(1) = 9 because 2^f(1) + 2^f(2) + ... + 2^f(9) = 2^0 + 2^0 + ... + 2^0 = 9;
a(2) = 108 because 2^f(1) + 2^f(2) + ... + 2^f(99) = 9*10 + 2*9 = 108, where f(10) = f(20) = ... = f(90) = 1 and f(i) = 0 otherwise.
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[(9/10)*(11^n-1): n in [1..20]]; // Vincenzo Librandi, Feb 15 2016
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for n from 1 to 100 do: x:=(9/10)*(11^n-1):printf(‘%d, ‘,x):od:
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Table[Table[(9/10) (11^n - 1), {n, 1, 20}]] (* Bruno Berselli, Feb 15 2016 *)
CoefficientList[Series[9/((1 - 11 x) (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Feb 15 2016 *)
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Vec(9*x/((1-11*x)*(1-x)) + O(x^30)) \\ Colin Barker, Feb 22 2016
A231591
Total number of 2's digits in primes less than 10^n.
Original entry on oeis.org
1, 3, 32, 391, 3906, 39572, 400626, 4047829, 40794211, 410514052, 4126066282, 41436122092, 415853103290, 4171375888398
Offset: 1
a(2)=3, since there are 3 2's in primes less than 100. Namely: 2, 23, 29.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 2, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231592
Total number of 3's digits in primes less than 10^n.
Original entry on oeis.org
1, 9, 75, 677, 6229, 58770, 564650, 5472472, 53396224, 523382007, 5148387363, 50778098799, 501864775685, 4968288427006
Offset: 1
a(2)=9, since there are 9 3's in primes less than 100. Namely: 3, 13, 23, 31, 37, 43, 53, 73, 83.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 3, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231593
Total number of 4's digits in primes less than 10^n.
Original entry on oeis.org
0, 3, 34, 360, 3772, 39006, 397474, 4022501, 40604951, 408986159, 4113511677, 41331763006, 414971464358, 4163826451096
Offset: 1
a(2)=3, since there are 3 4's in primes less than 100. Namely: 41, 43, 47.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 4, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231594
Total number of 5's digits in primes less than 10^n.
Original entry on oeis.org
1, 3, 33, 360, 3816, 38911, 396016, 4015732, 40543671, 408462140, 4109293287, 41296082801, 414669334188, 4161237526152
Offset: 1
a(2)=3, since there are 3 5's in primes less than 100. Namely: 5, 53, 59.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 5, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231595
Total number of 6's digits in primes less than 10^n.
Original entry on oeis.org
0, 2, 33, 369, 3741, 38714, 395621, 4007705, 40484195, 408035120, 4105718243, 41266320918, 414416274953, 4159068898063
Offset: 1
a(2)=2, since there are 2 6's in primes less than 100. Namely: 61, 67.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 6, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231596
Total number of 7's digits in primes less than 10^n.
Original entry on oeis.org
1, 9, 78, 652, 6172, 58327, 560506, 5443074, 53152746, 521422184, 5132090751, 50642752951, 500714890907, 4958432528817
Offset: 1
a(2)=9, since there are 9 7's in primes less than 100. Namely: 7, 17, 37, 47, 67, 71, 73, 79, 97.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 7, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
A231597
Total number of 8's digits in primes less than 10^n.
Original entry on oeis.org
0, 2, 30, 351, 3690, 38541, 394398, 3998411, 40399778, 407316676, 4099892369, 41217744252, 414006129652, 4155543234392
Offset: 1
a(2)=2, since there are 2 8's in primes less than 100. Namely: 83, 89.
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Table[Count[IntegerDigits[Prime[Range[PrimePi[10^n - 1]]]], 8, 2], {n, 7}] (* Robert Price, Jun 16 2019 *)
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