A065680 -id:A065680 - cp's OEIS frontend

A065681 Number of primes <= prime(n) which begin with a 2.

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			After 2 and 23, 29 is the third prime beginning with 2: A000040(10) = 29, therefore a(10) = 3. a(664579) = 77025 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045708, A065680.

Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 2] &, 87] (* Michael De Vlieger, Jun 14 2018 *)

lista(n) = { my(a=[p\10^logint(p,10)==2 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065682 Number of primes <= prime(n) which begin with a 3.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			a(1) = 0, a(2) = 1. a(664579) = 75290 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045709, A065680.

Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 3] &, 87] (* Michael De Vlieger, Jun 14 2018 *)

lista(n) = { my(a=[p\10^logint(p,10)==3 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065683 Number of primes <= prime(n) which begin with a 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			41 = A000040(13) is the first prime beginning with 4, so a(13) = 1. a(664579) = 74114 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045710, A065680.

Table[Count[Take[Prime[Range[100]],n],?(First[IntegerDigits[#]] == 4&)],{n,100}]  (* _Harvey P. Dale, Apr 18 2011 *)

lista(n) = { my(a=[p\10^logint(p,10)==4 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065684 Number of primes <= prime(n) which begin with a 5.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			a(i) = 1 for 2 < i < 16 and a(16) = 2 as 53 = A000040(16) is the second prime beginning with 5. a(664579) = 72951 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045711, A065680.

Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 5] &, 103] (* Michael De Vlieger, Jun 14 2018 *)

lista(n) = { my(a=[p\10^logint(p,10)==5 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065685 Number of primes <= prime(n) which begin with a 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			a(17) = 0, a(18) = 1: 61 = A000040(18) is the first prime beginning with 6. a(664579) = 72257 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045712, A065680.

Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 6] &, 105] (* Michael De Vlieger, Jun 14 2018 *)

lista(n) = { my(a=[p\10^logint(p,10)==6 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065686 Number of primes <= prime(n) which begin with a 7.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			a(3) = 0, a(4) = 1. a(664579) = 71564 (A000040(664579) = 9999991 is the largest prime < 10^7).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045713, A065680.

lista(n) = { my(a=[p\10^logint(p,10)==7 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

A065687 Number of primes <= prime(n) which begin with an 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Reinhard Zumkeller, Nov 13 2001

			83 = A000040(23) is the first prime beginning with an 8, so a(23) = 1 and a(i) = 0 for i < 23. a(664579) = 71038 (A000040(664579) = 9999991 is the largest prime < 10,000,000).

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000040, A045714, A065680.

Accumulate[If[First[IntegerDigits[#]] == 8, 1, 0]&/@Prime[Range[100]]] (* Vincenzo Librandi, Nov 28 2016 *)

lista(n) = { my(a=[p\10^logint(p,10)==8 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009

cp's OEIS Frontend

A065681 Number of primes <= prime(n) which begin with a 2.

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A065682 Number of primes <= prime(n) which begin with a 3.

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A065683 Number of primes <= prime(n) which begin with a 4.

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A065684 Number of primes <= prime(n) which begin with a 5.

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A065685 Number of primes <= prime(n) which begin with a 6.

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A065686 Number of primes <= prime(n) which begin with a 7.

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A065687 Number of primes <= prime(n) which begin with an 8.

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