cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A073505 Number of primes == 1 (mod 10) less than 10^n.

Original entry on oeis.org

0, 5, 40, 306, 2387, 19617, 166104, 1440298, 12711386, 113761519, 1029517130, 9401960980, 86516370000
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

Comments

Also Pi(n,5,1)
This and the related sequences A073505-A073517 and A006880, A073548-A073565 are included because there is interest in the distribution of primes by their initial or final digits.

Examples

			a(2) = 5 because there are 5 primes == 1 (mod 10) less than 10^2. They are 11, 31, 41, 61 and 71.
		

Crossrefs

Programs

  • Mathematica
    c = 0; k = 1; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

a(n) + A073506(n) + A073507(n) + A073508(n) + 2 = A006880(n).

Extensions

Edited by Robert G. Wilson v, Oct 03 2002
a(10) from Robert G. Wilson v, Dec 22 2003
a(11)-a(13) from Giovanni Resta, Aug 07 2018

A073506 Number of primes == 3 (mod 10) less than 10^n.

Original entry on oeis.org

1, 7, 42, 310, 2402, 19665, 166230, 1440474, 12712499, 113765625, 1029509448, 9401979904, 86516427946
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

Comments

Also Pi(n,5,3)
This and the related sequences A073505-A073517 and A006880, A073548-A073565 are included because there is interest in the distribution of primes by their initial or final digits.

Examples

			a(2)=7 because there are 7 primes == 3 (mod 10) less than 10^2. They are 3, 13, 23, 43, 53, 73 and 83.
		

Crossrefs

Programs

  • Mathematica
    c = 0; k = 3; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

A073505(n) + a(n) + A073507(n) + A073508(n) + 2 = A006880(n).

Extensions

Edited by Robert G. Wilson v, Oct 03 2002
a(10) from Robert G. Wilson v, Dec 22 2003
a(11)-a(13) from Giovanni Resta, Aug 07 2018

A073507 Number of primes == 7 (mod 10) less than 10^n.

Original entry on oeis.org

1, 6, 46, 308, 2411, 19621, 166211, 1440495, 12712314, 113764039, 1029518337, 9401997000, 86516367790
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

Comments

This and the related sequences A073505-A073517 and A006880, A073548-A073565 are included because there is interest in the distribution of primes by their initial or final digits.

Examples

			a(2)=6 because there are 6 primes == 7 (mod 10) less than 10^2. They are 7, 17, 37, 47, 67 and 97.
		

Crossrefs

Programs

  • Mathematica
    c = 0; k = 7; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

A073505(n) + A073506(n) + a(n) + A073508(n) + 2 = A006880(n).

Extensions

Edited by Robert G. Wilson v, Oct 03 2002
a(10) from Robert G. Wilson v, Dec 22 2003
a(11)-a(13) from Giovanni Resta, Aug 07 2018

A073508 Number of primes == 9 (mod 10) less than 10^n.

Original entry on oeis.org

0, 5, 38, 303, 2390, 19593, 166032, 1440186, 12711333, 113761326, 1029509896, 9401974132, 86516371101
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 14 2002

Keywords

Comments

This and the related sequences A073505-A073517 and A006880, A073548-A073565 are included because there is interest in the distribution of primes by their initial or final digits.

Examples

			a(2) = 5 because there are 5 primes == 9 (mod 10) less than 10^2. They are 19, 29, 59, 79 and 89.
		

Crossrefs

Programs

  • Mathematica
    c = 0; k = 9; Do[While[k < 10^n, If[PrimeQ[k], c++ ]; k += 10]; Print[c], {n, 1, 10}]

Formula

A073505(n) + A073506(n) + A073507(n) + a(n) + 2 = A006880(n).

Extensions

Edited by Robert G. Wilson v, Oct 03 2002
a(10) from Robert G. Wilson v, Dec 22 2003
a(11)-a(13) from Giovanni Resta, Aug 07 2018
Showing 1-4 of 4 results.