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 1-10 of 22 results. Next

A145480 Primes p such that (p+37)/2 is prime.

Original entry on oeis.org

37, 97, 109, 157, 181, 241, 277, 349, 409, 421, 577, 661, 709, 757, 829, 877, 937, 1009, 1117, 1201, 1249, 1381, 1429, 1609, 1621, 1669, 1777, 1801, 2029, 2089, 2137, 2221, 2269, 2389, 2437, 2521, 2557, 2617, 2857, 3049, 3061, 3121, 3181, 3217, 3301, 3361
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 1 mod 12

Links

Crossrefs

A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 37; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(37+#)/2]&] (* Harvey P. Dale, Jun 23 2016 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&isprime((37+p)/2), print(p,", "))) \\Anders Hellström, Jan 23 2017
  • PARI
    list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+37)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 23 2017

A145490 Numbers k such that 6k+19 is prime and absolute value of 12k+1 is also prime.

Original entry on oeis.org

-2, -1, 3, 8, 9, 13, 15, 20, 23, 29, 34, 35, 48, 55, 59, 63, 69, 73, 78, 84, 93, 100, 104, 115, 119, 134, 135, 139, 148, 150, 169, 174, 178, 185, 189, 199, 203, 210, 213, 218, 238, 254, 255, 260, 265, 268, 275, 280, 288, 289, 293, 294, 295, 308, 309, 335, 344
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145490.

Programs

  • Maple
    with(numtheory): a:=proc(n) if(isprime(6*n+19) and isprime(abs(12*n+1)))then return n: fi: return NULL: end: seq(a(n),n=-2..350); # Nathaniel Johnston, Jul 26 2011

Formula

a(n) = (A145480(n-2)-1)/12 for n >= 3.

Extensions

Corrected by Arkadiusz Wesolowski, Jul 26 2011

A063909 Primes p such that 2*p - 5 is also prime.

Original entry on oeis.org

5, 11, 17, 23, 29, 47, 53, 59, 71, 89, 101, 131, 137, 149, 179, 197, 227, 233, 257, 263, 281, 311, 353, 383, 389, 401, 431, 443, 467, 479, 491, 509, 557, 593, 599, 617, 641, 647, 653, 683, 719, 743, 809, 821, 857, 863, 941, 947, 953, 977, 1109
Offset: 1

Views

Author

N. J. A. Sloane, Aug 31 2001

Keywords

Comments

All terms are == 5 (mod 6). - Zak Seidov, Jan 07 2014
There are several interesting computer generated conjectures for this sequence at Jon Maiga's Sequence Machine site. - Antti Karttunen, Dec 07 2021
Note that 5, p, 2p - 5 form an arithmetic progression (PAP-3). - Charles R Greathouse IV, Mar 03 2025

Examples

			29 is in the sequence since p = 29 is prime and 2*p - 5 = 53 is also prime.

Links

Crossrefs

Subsequence of A007528 and hence A016969.
Cf. A000040, A089253, A145471.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime(2*p-5)]; // Vincenzo Librandi, Feb 25 2016
  • Mathematica
    Select[Prime[Range[500]],PrimeQ[2#-5]&] (* Harvey P. Dale, Oct 10 2011 *)
  • PARI
    { n=0; p=1; for (m=1, 10^9, p=nextprime(p+1); if (isprime(2*p - 5), write("b063909.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 02 2009
  • PARI
    isA063909(p) = ((p%2)&&isprime(p)&&isprime(p+p-5)); \\ Antti Karttunen, Dec 07 2021
  • PARI
    list(lim)=my(v=List()); forprimestep(p=5,lim\1,6, if(isprime(2*p-5), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 03 2025

Formula

Intersection of A089253 and A000040. - Michael B. Porter, Jan 07 2014
a(n) = (A145471(n)+5)/2. [Also listed by Sequence Machine, and obviously true] - Antti Karttunen, Dec 07 2021

A145475 Primes p such that (17+p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 41, 89, 101, 149, 197, 257, 281, 317, 449, 461, 509, 521, 569, 617, 677, 701, 761, 821, 881, 941, 1097, 1109, 1181, 1217, 1277, 1289, 1301, 1601, 1637, 1697, 1709, 1877, 1889, 1949, 2081, 2309, 2357, 2417, 2441, 2549, 2621, 2729, 2801, 2837, 2861
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(17+#)/2]&] (* Harvey P. Dale, Jan 02 2013 *)

A145472 Primes p such that (p+7)/2 is prime.

Original entry on oeis.org

3, 7, 19, 31, 67, 79, 127, 139, 151, 199, 211, 271, 307, 379, 439, 547, 607, 619, 691, 727, 739, 751, 787, 811, 859, 907, 919, 967, 991, 1039, 1087, 1231, 1279, 1447, 1459, 1471, 1531, 1567, 1699, 1747, 1759, 1831, 1867, 1987, 2011, 2131, 2179, 2239, 2251
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first one) to 7 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480, A063910.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)| IsPrime((p + 7) div 2)]; // Vincenzo Librandi, Feb 04 2013
  • Mathematica
    aa = {}; k = 7; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+7)/2]&] (* Harvey P. Dale, Jan 11 2020 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&isprime((7+p)/2), print1(n, ", "))) \\Anders Hellström, Jan 23 2017
  • PARI
    list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+7)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

A145474 Primes p such that (13+p)/2 is prime.

Original entry on oeis.org

13, 61, 73, 109, 181, 193, 241, 313, 349, 373, 409, 433, 541, 601, 613, 661, 733, 829, 853, 1033, 1069, 1129, 1201, 1213, 1249, 1453, 1489, 1609, 1693, 1741, 1753, 1801, 1861, 2029, 2053, 2089, 2113, 2161, 2221, 2293, 2389, 2593, 2749, 2833, 2953, 3049
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 1 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Maple
    select(t -> isprime(t) and isprime((13+t)/2), [seq(12*k+1, k=1..100)]); # Robert Israel, Aug 05 2014
  • Mathematica
    aa = {}; k = 13; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
  • PARI
    forprime(p=3,10^4,if(isprime((13+p)/2),print1(p,", "))) \\ Derek Orr, Aug 05 2014

A145476 Primes p such that (19 + p)/2 is prime.

Original entry on oeis.org

3, 7, 19, 43, 67, 103, 127, 139, 199, 283, 307, 367, 379, 439, 463, 523, 547, 607, 643, 727, 739, 823, 859, 907, 1063, 1123, 1303, 1327, 1399, 1447, 1459, 1483, 1627, 1699, 1747, 1999, 2083, 2239, 2287, 2383, 2539, 2887, 3067, 3079, 3307, 3319, 3463, 3499
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(#+19)/2]&] (* Harvey P. Dale, Sep 06 2023 *)
  • PARI
    list(n)=my(t=1,p,i=1);while(i2&&bigomega((19+p)/2)==1,print(p))) \\ Anders Hellström, Jan 22 2017

A145477 Primes p such that (23 + p)/2 is prime.

Original entry on oeis.org

3, 11, 23, 59, 71, 83, 179, 191, 239, 251, 311, 359, 431, 443, 479, 491, 503, 563, 599, 683, 743, 839, 863, 911, 983, 1019, 1091, 1103, 1151, 1163, 1259, 1283, 1499, 1523, 1571, 1619, 1871, 1931, 2003, 2039, 2099, 2339, 2351, 2411, 2423, 2531, 2543, 2579
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 11 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(23+#)/2]&] (* Harvey P. Dale, Jan 26 2024 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&prime((23+p)/2), print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A145478 Primes p such that (29 + p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 53, 89, 113, 137, 149, 173, 197, 233, 269, 317, 353, 449, 509, 557, 593, 677, 773, 809, 857, 929, 953, 977, 1013, 1097, 1109, 1277, 1289, 1373, 1409, 1493, 1613, 1697, 1733, 1877, 1913, 1997, 2069, 2153, 2273, 2297, 2333, 2357, 2417, 2549, 2609
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 29; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
  • PARI
    first(n)=my(t=1, p, i=1); while(i2&&isprime((29+p)/2), print1(p,", "))) \\ Anders Hellström, Jan 22 2017

A165138 Smallest prime p > prime(n) such that p+prime(n) is a semiprime.

Original entry on oeis.org

7, 7, 17, 19, 23, 61, 29, 43, 59, 53, 43, 97, 53, 79, 59, 89, 83, 73, 79, 107, 181, 127, 131, 113, 109, 113, 151, 167, 193, 149, 151, 167, 197, 163, 197, 163, 229, 199, 179, 281, 347, 241, 263, 229, 257, 223, 271, 331, 239, 313, 269, 263, 313, 263, 269, 359, 293
Offset: 1

Views

Author

Zak Seidov, Sep 04 2009

Keywords

Comments

Except for having an additional first term the sequence coincides with A084704.
For n>2, a(n)-prime(n) is a multiple of 12, e.g., 17-5, 19-7, 23-11, etc. - Zak Seidov, Oct 15 2015

Examples

			2+7=9=3*3 (semiprime), 3+7=10=2*5 (semiprime), 5+17=22=2*11 (semiprime).

Links

Crossrefs

Cf. A084704, A001358, A145471.

Programs

  • Mathematica
    sp[n_]:=Module[{np=NextPrime[n]},While[PrimeOmega[n+np]!=2,np= NextPrime[ np]]; np]; sp/@Prime[Range[60]] (* Harvey P. Dale, Apr 06 2016 *)
  • PARI
    a(n) = {q = prime(n); p = nextprime(q+1); while (bigomega(p+q)!=2, p = nextprime(p+1)); p;} \\ Michel Marcus, Oct 15 2015

Extensions

Prior Mathematica program deleted by Harvey P. Dale, Apr 06 2016
Showing 1-10 of 22 results. Next

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

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