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 1-3 of 3 results.

A302434 Number of primes of the form b^2 + 2 for b <= 10^n.

Original entry on oeis.org

4, 12, 69, 447, 3423, 27869, 236985, 2054022, 18127693, 162237123
Offset: 1

Views

Author

Seiichi Manyama, Apr 07 2018

Keywords

Comments

From Jacques Tramu, Sep 13 2018: (Start)
Table C(i) = a(i)/(n*log(n)), with n = 10^i:
a(1) = 4 C(1) = 0.92103404
a(2) = 12 C(2) = 0.55262042
a(3) = 69 C(3) = 0.47663511
a(4) = 447 C(4) = 0.41170221
a(5) = 3423 C(5) = 0.39408744
a(6) = 27869 C(6) = 0.38502446
a(7) = 236985 C(7) = 0.38197469
a(8) = 2054022 C(8) = 0.37836484
a(9) = 18127693 C(9) = 0.37566500
a(10) = 162237123 C(10) = 0.37356478
(End)

Examples

			a(1) = 4 because there are 4 primes of the form b^2+2 for b <= 10: 2, 3, 11 and 83.

Crossrefs

Number of primes of the form b^2+m for b <= 10^n: A302443 (m=-3), A302442 (m=-2), A206709 (m=1), this sequence (m=2), A302435 (m=3).
Cf. A056899.

Programs

  • PARI
    {a(n) = sum(k=0, 10^n, isprime(k^2+2))}

Extensions

a(10) from Jacques Tramu, Sep 13 2018

A302435 Number of primes of the form b^2+3 for b <= 10^n.

Original entry on oeis.org

5, 18, 110, 712, 5427, 44096, 373019, 3228862, 28494961
Offset: 1

Views

Author

Seiichi Manyama, Apr 07 2018

Keywords

Examples

			a(1) = 5 because there are 5 primes of the form b^2+3 for b <= 10: 3, 7, 19, 67 and 103.

Crossrefs

Number of primes of the form b^2+m for b <= 10^n: A302443 (m=-3), A302442 (m=-2), A206709 (m=1), A302434 (m=2), this sequence (m=3).
Cf. A049423.

Programs

  • PARI
    {a(n) = sum(k=0, 10^n, isprime(k^2+3))}

A302443 Number of primes of the form b^2-3 for b <= 10^n.

Original entry on oeis.org

3, 19, 119, 849, 6663, 54514, 460019, 3982973, 35174007
Offset: 1

Views

Author

Seiichi Manyama, Apr 08 2018

Keywords

Examples

			a(1) = 3 because there are 3 primes of the form b^2-3 for b <= 10 : 13, 61 and 97.

Crossrefs

Number of primes of the form b^2+m for b <= 10^n: this sequence (m=-3), A302442 (m=-2), A206709 (m=1), A302434 (m=2), A302435 (m=3).
Cf. A028874.

Programs

  • PARI
    {a(n) = sum(k=0, 10^n, isprime(k^2-3))}
Showing 1-3 of 3 results.

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