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.

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A145473 Primes p such that (11 + p)/2 is prime.

Original entry on oeis.org

3, 11, 23, 47, 71, 83, 107, 131, 167, 191, 251, 263, 347, 383, 443, 467, 491, 503, 683, 827, 887, 911, 947, 971, 1031, 1103, 1163, 1187, 1223, 1283, 1307, 1427, 1511, 1583, 1607, 1667, 1811, 1847, 1871, 1931, 2027, 2087, 2111, 2207, 2351, 2423, 2447, 2543
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 = 11; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+11)/2]&] (* Harvey P. Dale, Apr 15 2012 *)
  • PARI
    first(n)=my(t=1, p, i=1); while(i2&&isprime((11+p)/2), print1(p,", "))) \\ Anders Hellström, Jan 22 2017

A145479 Primes p such that (31+p)/2 is prime.

Original entry on oeis.org

3, 7, 31, 43, 103, 127, 163, 223, 271, 283, 331, 367, 523, 631, 643, 727, 787, 811, 883, 967, 1051, 1063, 1123, 1171, 1231, 1291, 1423, 1447, 1471, 1483, 1543, 1627, 1723, 1783, 1951, 1987, 2011, 2143, 2203, 2311, 2371, 2467, 2551, 2731, 2767, 2887, 3067
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All terms are congruent to 3 mod 4 and (with the exception of the first term) to 7 mod 12.

Links

Crossrefs

Cf. A092109, A145471, A145472, A145473, A145474, A145475, A145476, A145477, A145478, A145479, A155480.

Programs

  • Mathematica
    aa = {}; k = 31; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(31+#)/2]&] (* Harvey P. Dale, Feb 05 2012 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&isprime((31+p)/2),print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A145487 Numbers k such that 6k+5 is prime and 12k+5 is also prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 11, 14, 16, 21, 22, 24, 29, 32, 37, 38, 42, 43, 46, 51, 58, 63, 64, 66, 71, 73, 77, 79, 81, 84, 92, 98, 99, 102, 106, 107, 108, 113, 119, 123, 134, 136, 142, 143, 156, 157, 158, 162, 184, 191, 196, 198, 203, 212, 217, 219, 227, 228, 238, 241, 246
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (Prime[n] - 5)/12]], {n, 1, 500}]; aa
Select[Range[0, 250], PrimeQ[6 # + 5] && PrimeQ[12 # + 5] &] (* Ivan Neretin, Jan 21 2017 *)
Select[Range[0,250],AllTrue[5+{6#,12#},PrimeQ]&] (* Harvey P. Dale, Dec 20 2022 *)

Formula

a(n) = (A145471(n)-5)/12.

A308169 Numbers k such that A023896(k) mod A000203(k) is prime.

Original entry on oeis.org

3, 7, 10, 11, 16, 19, 22, 23, 25, 27, 31, 34, 43, 46, 49, 58, 59, 71, 79, 82, 83, 94, 100, 103, 106, 118, 121, 131, 139, 142, 163, 166, 178, 191, 199, 202, 208, 211, 214, 223, 226, 251, 262, 271, 274, 298, 311, 331, 334, 346, 358, 359, 379, 382, 383, 394, 419, 443, 454, 463, 466, 478, 479, 484
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, May 15 2019

Keywords

Comments

Numbers k such that (k*A000010(k)/2) mod A000203(k) is prime.
The primes in the sequence are A092109.
The even semiprimes in the sequence are A112774.

Examples

			a(3)=10 is in the sequence because A023896(10) mod A000203(10) = 20 mod 6 = 2, and 2 is prime.

Links

Crossrefs

Cf. A000010, A000203, A023896, A092109, A112774.

Programs

  • Maple
    select(n -> isprime((n*numtheory:-phi(n)/2) mod numtheory:-sigma(n)), [$2..1000]);
  • PARI
    isok(n) = isprime(n*eulerphi(n)/2 % sigma(n)); \\ Michel Marcus, May 15 2019

A338410 Primes p such that (p+2)/3 and (p+3)/2 are prime.

Original entry on oeis.org

7, 19, 31, 139, 199, 211, 379, 499, 631, 919, 1039, 1291, 1399, 1759, 2179, 2719, 2731, 2971, 3271, 3691, 4591, 5791, 5851, 6079, 7591, 8011, 8779, 10039, 11299, 11719, 11731, 12979, 14251, 15031, 15511, 15679, 18451, 18859, 20071, 21379, 21559, 22051, 22639, 23599, 24499, 24691, 25339, 25579
Offset: 1

Views

Author

J. M. Bergot and Robert Israel, Oct 25 2020

Keywords

Comments

All terms == 7 (mod 12).

Examples

			a(3) = 31 is in the sequence because 31, (31+2)/3 = 11 and ((31+3)/2) = 17 are prime.

Links

Crossrefs

Intersection of A091180 and A092109.

Programs

  • Maple
    filter:= t -> isprime(t) and isprime((t+2)/3) and isprime((t+3)/2):
select(filter, [seq(i,i=7..30000,12)]);
  • Mathematica
    Select[Prime[Range[3000]],AllTrue[{(#+2)/3,(#+3)/2},PrimeQ]&] (* Harvey P. Dale, May 20 2023 *)
  • PARI
    isok(p) = iferr(isprime(p) && isprime((p+2)/3) && isprime((p+3)/2), E, 0); \\ Michel Marcus, Oct 25 2020

A348421 Primes p == 3 (mod 4) such that (p+3)/2 is not prime.

Original entry on oeis.org

47, 67, 107, 127, 151, 167, 179, 227, 239, 263, 283, 307, 347, 367, 431, 439, 467, 487, 491, 503, 547, 571, 587, 599, 607, 643, 647, 683, 719, 727, 739, 751, 787, 811, 823, 827, 887, 907, 947, 967, 983, 991, 1019, 1031, 1051, 1063, 1087, 1103, 1163, 1187
Offset: 1

Views

Author

Jianing Song, Oct 18 2021

Keywords

Comments

Complement of A092109 with respect to A002145.

Examples

			47 is a term since it is a prime congruent to 3 modulo 4 and (47+3)/2 = 25 is composite.

Links

Crossrefs

Cf. A002145, A092109, A348423.

Programs

  • Mathematica
    Select[4*Range[0, 300] + 3, PrimeQ[#] && ! PrimeQ[(# + 3)/2] &] (* Amiram Eldar, Oct 18 2021 *)
  • PARI
    isA348421(n) = isprime(n) && (n%4==3) && !isprime((n+3)/2)

Formula

a(n) = 2*A348423(n) - 3.

A015819 Numbers k such that phi(k + 3) | sigma(k).

Original entry on oeis.org

3, 6, 7, 11, 15, 19, 21, 23, 27, 31, 33, 42, 43, 51, 57, 59, 62, 69, 70, 71, 77, 79, 83, 84, 87, 93, 103, 131, 139, 141, 159, 163, 165, 177, 187, 189, 191, 199, 211, 213, 223, 235, 237, 251, 267, 270, 271, 282, 285, 287, 297, 311, 315, 316, 321, 330, 331
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A056097.
Contains A092109.

Programs

  • Maple
    select(t -> (numtheory:-sigma(t)/numtheory:-phi(t+3))::integer, [$1..1000]); # Robert Israel, Dec 13 2018
  • Mathematica
    Select[Range[1000], Divisible[DivisorSigma[1, #], EulerPhi[3 + #]] &] (* David Nacin, Mar 01 2012 *)
  • PARI
    is(n)=sigma(n)%(eulerphi(n+3))==0 \\ Charles R Greathouse IV, Sep 25 2012

A145481 Primes p such that 2*p - 17 is prime.

Original entry on oeis.org

11, 17, 23, 29, 53, 59, 83, 107, 137, 149, 167, 233, 239, 263, 269, 293, 317, 347, 359, 389, 419, 449, 479, 557, 563, 599, 617, 647, 653, 659, 809, 827, 857, 863, 947, 953, 983, 1049, 1163, 1187, 1217, 1229, 1283, 1319, 1373, 1409, 1427, 1439, 1487, 1493
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 250, And[PrimeQ@ #, # > 0] &[2 # - 17] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145475(n) - 17.

A145482 Primes p such that 2*p - 19 is prime.

Original entry on oeis.org

11, 13, 19, 31, 43, 61, 73, 79, 109, 151, 163, 193, 199, 229, 241, 271, 283, 313, 331, 373, 379, 421, 439, 463, 541, 571, 661, 673, 709, 733, 739, 751, 823, 859, 883, 1009, 1051, 1129, 1153, 1201, 1279, 1453, 1543, 1549, 1663, 1669, 1741, 1759, 1783, 1789
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 300, And[PrimeQ@ #, # > 0] &[2 # - 19] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145476(n) - 19.

A145483 Primes p such that 2*p - 23 is prime.

Original entry on oeis.org

13, 17, 23, 41, 47, 53, 101, 107, 131, 137, 167, 191, 227, 233, 251, 257, 263, 293, 311, 353, 383, 431, 443, 467, 503, 521, 557, 563, 587, 593, 641, 653, 761, 773, 797, 821, 947, 977, 1013, 1031, 1061, 1181, 1187, 1217, 1223, 1277, 1283, 1301, 1307, 1361
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 240, And[PrimeQ@ #, # > 0] &[2 # - 23] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145477(n) - 23.
Previous Showing 11-20 of 26 results. Next

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