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 1-9 of 9 results.

A118915 Primes p such that (p^2 + 5)/6 is prime.

Original entry on oeis.org

5, 13, 19, 23, 37, 41, 89, 113, 127, 131, 139, 149, 167, 197, 229, 233, 239, 251, 271, 359, 373, 401, 433, 449, 463, 503, 523, 541, 607, 631, 643, 653, 701, 719, 743, 769, 811, 827, 877, 881, 887, 919, 967, 971, 1009, 1013, 1021, 1093, 1097, 1283, 1301
Offset: 1

Views

Author

T. D. Noe, May 05 2006

Keywords

Comments

For all primes q>3, we have q=6k+-1 for some k, which makes it easy to show that 6 divides q^2+5.
(n^2+5)/6 is an integer for all primes except 2 and 3. - Michael B. Porter, Apr 14 2010

Crossrefs

Cf. A109953 (primes p such that (p^2+1)/3 is prime), A118918 (primes p such that (p^2+11)/12 is prime).

Programs

A118940 Primes p such that (p^2+7)/8 is prime.

Original entry on oeis.org

3, 7, 17, 23, 41, 47, 71, 89, 103, 113, 127, 137, 151, 191, 193, 199, 223, 263, 271, 281, 337, 359, 401, 439, 457, 503, 521, 569, 577, 599, 641, 719, 727, 751, 839, 857, 863, 881, 887, 929, 991, 1009, 1033, 1097, 1103, 1151, 1193, 1217, 1231, 1279, 1297, 1303
Offset: 1

Views

Author

T. D. Noe, May 06 2006

Keywords

Comments

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 8 divides q^2+7.

Crossrefs

Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118941 and A118942.

Programs

  • Mathematica
    Select[Prime[Range[200]],PrimeQ[(#^2+7)/8]&]
  • PARI
    lista(nn) = {forprime(p=2, nn, iferr(if (isprime(q=(p^2+7)/8), print1(q, ", ")), E, ););} \\ Michel Marcus, Feb 18 2018

A118939 Primes p such that (p^2+3)/4 is prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 29, 31, 41, 43, 67, 83, 101, 109, 139, 151, 157, 179, 181, 199, 211, 223, 239, 263, 277, 283, 307, 311, 337, 347, 353, 379, 389, 419, 431, 463, 491, 557, 577, 587, 619, 659, 673, 739, 757, 797, 809, 811, 829, 853, 907, 911, 953, 991, 1051
Offset: 1

Views

Author

T. D. Noe, May 06 2006

Keywords

Comments

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 4 divides q^2+3. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118940, A118941 and A118942.

Programs

  • Mathematica
    Select[Prime[Range[200]],PrimeQ[(#^2+3)/4]&]

A241120 Primes p such that (p^3 + 2)/3 is prime.

Original entry on oeis.org

13, 19, 31, 193, 211, 223, 229, 271, 331, 571, 619, 691, 739, 751, 853, 991, 1009, 1039, 1051, 1231, 1303, 1321, 1549, 1741, 1789, 1831, 1993, 1999, 2029, 2089, 2113, 2143, 2203, 2311, 2521, 2551, 2683, 2749, 2851, 3121, 3259, 3331, 3571, 3631, 3823, 3853, 4093
Offset: 1

Views

Author

K. D. Bajpai, Apr 16 2014

Keywords

Examples

			13 is prime and appears in the sequence because (13^3 + 2)/3 = 733 which is a prime.
31 is prime and appears in the sequence because (31^3 + 2)/3 = 9931 which is a prime.

Links

Crossrefs

Cf. A109953 (primes p: (p^2+1)/3 is prime).
Cf. A118915 (primes p: (p^2+5)/6 is prime).
Cf. A118918 (primes p: (p^2+11)/12 is prime).
Cf. A241101 (primes p: (p^3-4)/3 is prime).

Programs

  • Maple
    KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+2)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
  • Mathematica
    Select[Prime[Range[500]], PrimeQ[(#^3 + 2)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 2)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}]          (* b-file *)
  • PARI
    s=[]; forprime(p=2, 8000, if((p^3+2)%3==0 && isprime((p^3+2)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014

A118941 Primes p such that (p^2-5)/4 is prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 31, 41, 43, 53, 61, 71, 79, 83, 89, 97, 101, 107, 109, 113, 131, 137, 167, 173, 179, 193, 229, 241, 251, 263, 269, 277, 281, 283, 307, 311, 317, 349, 353, 373, 383, 419, 431, 439, 461, 463, 467, 563, 571, 577, 593, 607, 613, 619, 647
Offset: 1

Views

Author

T. D. Noe, May 06 2006

Keywords

Comments

For all primes q>2, we have q=4k+-1 for some k, which makes it easy to show that 4 divides q^2-5. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118940 and A118942.

Programs

  • Mathematica
    Select[Prime[Range[200]],PrimeQ[(#^2-5)/4]&]

A118942 Primes p such that (p^2-13)/12 is prime.

Original entry on oeis.org

7, 13, 17, 19, 23, 31, 37, 41, 53, 67, 71, 73, 89, 103, 107, 113, 131, 139, 157, 163, 181, 199, 211, 233, 239, 257, 269, 283, 307, 311, 337, 359, 373, 379, 401, 419, 463, 487, 491, 499, 509, 521, 577, 593, 607, 617, 631, 647, 653, 683, 701, 733, 761, 769, 787
Offset: 1

Views

Author

T. D. Noe, May 06 2006

Keywords

Comments

For all primes q>3, we have q=6k+-1 for some k, which makes it easy to show that 12 divides q^2-13. Similar sequences, with p and (p^2+a)/b both prime, are A048161, A062324, A062326, A062718, A109953, A110589, A118915, A118918, A118939, A118940 and A118941.

Programs

  • Mathematica
    Select[Prime[Range[200]],PrimeQ[(#^2-13)/12]&]

A241101 Primes p such that (p^3 - 4)/3 is prime.

Original entry on oeis.org

7, 31, 37, 43, 61, 73, 97, 103, 157, 163, 211, 277, 331, 337, 457, 487, 613, 661, 733, 751, 811, 883, 991, 1021, 1093, 1297, 1321, 1483, 1693, 1741, 1873, 2083, 2113, 2143, 2203, 2221, 2287, 2347, 2437, 2473, 2707, 2917, 3001, 3067, 3187, 3307, 3331, 3343, 3541
Offset: 1

Views

Author

K. D. Bajpai, Apr 16 2014

Keywords

Examples

			7 is prime and appears in the sequence because (7^3 - 4)/3 = 113 which is a prime.
31 is prime and appears in the sequence because (31^3 - 4)/3 = 9929 which is a prime.

Links

Crossrefs

Cf. A109953 (primes p: (p^2+1)/3 is prime).
Cf. A118915 (primes p: (p^2+5)/6 is prime).
Cf. A118918 (primes p: (p^2+11)/12 is prime).

Programs

  • Maple
    KD:= proc() local a,b;a:=ithprime(n); b:=(a^3-4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
  • Mathematica
    Select[Prime[Range[500]], PrimeQ[(#^3 - 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 - 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)
  • PARI
    s=[]; forprime(p=2, 4000, if((p^3-4)%3==0 && isprime((p^3-4)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014

A235705 Primes p such that (p^3 + 6)/5 is prime.

Original entry on oeis.org

19, 59, 269, 349, 409, 419, 479, 769, 929, 1109, 1319, 1399, 1979, 2609, 3659, 4079, 4919, 5309, 5449, 5879, 6079, 6299, 6949, 7069, 7129, 7229, 7699, 7829, 8069, 8329, 8599, 9679, 10729, 11969, 12809, 13109, 13229, 13859, 14159, 14419, 14629, 14929, 15259
Offset: 1

Views

Author

K. D. Bajpai, Apr 20 2014

Keywords

Comments

All the terms in the sequence are congruent to 1 or 3 mod 4.

Examples

			a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime.
a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.

Links

Crossrefs

Cf. A109953 (primes p: (p^2+1)/3 is prime).
Cf. A118915 (primes p: (p^2+5)/6 is prime).
Cf. A118918 (primes p: (p^2+11)/12 is prime).
Cf. A241101 (primes p: (p^3-4)/3 is prime).
Cf. A241120 (primes p: (p^3+2)/3 is prime).

Programs

  • Maple
    KD:= proc() local a,b; a:=ithprime(n); b:=(a^3+6)/5; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..5000);
  • Mathematica
    Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)
  • PARI
    s=[]; forprime(p=2, 20000, if((p^3+6)%5==0 && isprime((p^3+6)/5), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014

A241099 Primes p such that (p^3 + 4)/3 is prime.

Original entry on oeis.org

5, 23, 53, 113, 173, 197, 269, 317, 383, 443, 557, 563, 587, 647, 659, 773, 797, 827, 947, 983, 1097, 1103, 1187, 1217, 1229, 1889, 1913, 1949, 2039, 2099, 2153, 2213, 2339, 2357, 2399, 2417, 2447, 2579, 2693, 2837, 2879, 2897, 2903, 2939, 2969, 3089, 3203
Offset: 1

Views

Author

K. D. Bajpai, Apr 15 2014

Keywords

Examples

			5 is prime and appears in the sequence because (5^3 + 4)/3 = 43 which is a prime.
23 is prime and appears in the sequence because (23^3 + 4)/3 = 4057 which is a prime.

Links

Crossrefs

Cf. A109953 (primes p:(p^2+1)/3 is prime).
Cf. A118915 (primes p:(p^2+5)/6 is prime).
Cf. A118918 (primes p:(p^2+11)/12 is prime).

Programs

  • Maple
    KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
  • Mathematica
    Select[Prime[Range[500]], PrimeQ[(#^3 + 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.