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 16 results. Next

A092551 Duplicate of A033560.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 29, 37, 43, 47, 59, 73, 79, 83, 89, 103, 107, 113, 127, 139, 149, 157, 167, 173, 199, 227, 233, 239, 257, 269, 283, 293, 307, 313, 349, 359, 373, 397, 409, 419, 433, 439, 443, 463, 467, 479, 499, 523, 547, 563, 569, 577, 593, 607, 617, 619
Offset: 1

Views

Author

Giovanni Teofilatto, Apr 09 2004

Keywords

A156104 Primes p such that p+36 is also prime.

Original entry on oeis.org

5, 7, 11, 17, 23, 31, 37, 43, 47, 53, 61, 67, 71, 73, 101, 103, 113, 127, 131, 137, 157, 163, 191, 193, 197, 227, 233, 241, 257, 271, 277, 281, 311, 313, 317, 331, 337, 347, 353, 373, 383, 397, 421, 431, 443, 463, 467, 487, 521, 541, 557, 563, 571, 577, 607
Offset: 1

Views

Author

Vincenzo Librandi, Feb 08 2009

Keywords

Links

Crossrefs

Cf. A156112.
Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), A252089 (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), this sequence (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

Programs

  • Magma
    [p: p in PrimesUpTo(1000) | IsPrime(p + 36)]; // Vincenzo Librandi, Oct 31 2012
  • Mathematica
    Select[Prime[Range[1000]], PrimeQ[(#+ 36)]&] (* Vincenzo Librandi, Oct 31 2012 *)

A242476 Primes p such that p + 22 is also prime.

Original entry on oeis.org

7, 19, 31, 37, 61, 67, 79, 109, 127, 151, 157, 211, 229, 241, 271, 331, 337, 367, 379, 397, 409, 421, 439, 457, 487, 499, 541, 547, 571, 577, 619, 631, 661, 739, 751, 787, 859, 907, 919, 991, 997, 1009, 1039, 1069, 1087, 1129, 1171, 1201, 1237, 1279, 1297
Offset: 1

Views

Author

Vincenzo Librandi, May 21 2014

Keywords

Links

Crossrefs

Cf. A033560, A079021, A153419.

Programs

  • Magma
    [p: p in PrimesUpTo(1500)| IsPrime(p+22)];
  • Mathematica
    Select[Prime[Range[900]], PrimeQ[# + 22] &]

A252089 Primes p such that p + 26 is prime.

Original entry on oeis.org

3, 5, 11, 17, 41, 47, 53, 71, 83, 101, 113, 131, 137, 167, 173, 197, 251, 257, 281, 311, 347, 353, 383, 431, 461, 521, 587, 593, 617, 647, 683, 701, 743, 761, 797, 827, 857, 881, 911, 941, 971, 983, 1013, 1061, 1091, 1097, 1103, 1187, 1223, 1277, 1301, 1373
Offset: 1

Views

Author

Vincenzo Librandi, Dec 14 2014

Keywords

Examples

			17 is in this sequence because 17+26 = 43 is prime.
431 is in this sequence because 431+26 = 457 is prime.

Links

Crossrefs

Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), this sequence (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), A156104 (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

Programs

  • Magma
    [NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+26)];
  • Mathematica
    Select[Prime[Range[200]], PrimeQ[# + 26] &]

A054982 a(n) = least composite number such that sigma(a(n)+n!) = sigma(a(n))+n! where sigma() = A000203.

Original entry on oeis.org

434, 104, 80, 182, 427, 1727, 4147, 7163, 42031, 165841, 569257, 2683909, 10040081, 39094849, 155533969, 717519401, 3041377519, 16076525809, 71749935913
Offset: 2

Views

Author

Labos Elemer, May 29 2000

Keywords

Comments

a(21) <= 328823468719, a(22) <= 1542201899569, a(23) <= 9325753929619. - Donovan Johnson, Sep 22 2013

Examples

			a(7) = 1727 = 11*157, 4 divisors, sigma(1727)+5040 = 1896+5040 = 6936, sigma(1727+5040) = sigma(6767) = 1+67+101+6767 = 6936.
a(2) = A054799(24) = 434, a(3) = A015914(19) = 104, the first composites in that series.

Crossrefs

Cf. A054904, A054905, A054799, A015914, A033560.

Programs

  • Mathematica
    L = {}; Do[i = 1; While[ ! ((Plus @@ Divisors[i + j! ] == j! + Plus @@ Divisors[i]) && ! PrimeQ[i]), i++ ]; L = Append[L, i], {j, 2, 13}]; L (from Vit Planocka)

Extensions

More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 22 2003
a(14)-a(19) from Donovan Johnson, Nov 30 2008
a(20) from Donovan Johnson, Sep 19 2013

A054984 Composite numbers k such that sigma(k + 6!) = sigma(k + 720) = sigma(k) + 720.

Original entry on oeis.org

427, 553, 595, 623, 737, 871, 913, 923, 1199, 1207, 1241, 1507, 1582, 1817, 1848, 2193, 2226, 2337, 2398, 2407, 2553, 2561, 2728, 2758, 2929, 3016, 3115, 3248, 3346, 3502, 3503, 3598, 3705, 3762, 4171, 4293, 4343, 4462, 4587, 4633, 4841, 4867, 4984
Offset: 1

Views

Author

Labos Elemer, May 29 2000

Keywords

Examples

			553 is a term because sigma(553) + 720 = 640 + 720 = 1360 = sigma(553 + 720) = sigma(1273) = 1 + 19 + 67 + 1273.

Links

Crossrefs

Cf. A015914, A015915, A015916, A015917, A033560, A033561, A054799.

Programs

  • Mathematica
    Select[Range[5000], CompositeQ[#] && Differences@ DivisorSigma[1, {#, # + 720}] == {720} &] (* Amiram Eldar, Mar 09 2025 *)
  • PARI
    isok(k) = !isprime(k) && sigma(k + 720) == sigma(k) + 720; \\ Amiram Eldar, Mar 09 2025

A054985 Composite numbers x such that sigma(x+120) = sigma(x)+120.

Original entry on oeis.org

182, 203, 287, 350, 407, 558, 611, 731, 779, 803, 963, 1424, 1643, 2627, 2747, 3431, 3806, 4187, 4223, 5063, 6767, 7946, 8927, 9047, 11904, 12707, 12878, 15794, 18923, 20567, 27263, 31175, 32111, 34427, 43139, 43811, 45854, 50165, 52592, 57479
Offset: 1

Views

Author

Labos Elemer, May 29 2000

Keywords

Comments

See also A015914, A054799, A033560.

Examples

			a(6)=558, sigma(558)+120=1248+120=1368=sigma(678)=sigma(558+120).

Links

Crossrefs

Cf. A015914-A015917, A054799.

Programs

  • Mathematica
    Select[Range[60000],CompositeQ[#]&&DivisorSigma[1,#]+120 == DivisorSigma[ 1,#+120]&] (* Harvey P. Dale, Nov 25 2022 *)
  • PARI
    isok(n) = !isprime(n) && (sigma(n+120) == (sigma(n) + 120)); \\ Michel Marcus, Dec 31 2013

A185022 Prime p such that p, p+12, p+24 are all primes.

Original entry on oeis.org

5, 7, 17, 19, 29, 47, 59, 89, 127, 139, 167, 199, 227, 239, 257, 269, 397, 409, 419, 467, 479, 607, 619, 727, 797, 929, 997, 1009, 1039, 1277, 1279, 1427, 1447, 1459, 1487, 1499, 1559, 1597, 1697, 1709, 1777, 1877, 1889, 1987, 2087, 2129, 2269, 2399, 2609
Offset: 1

Views

Author

Salvatore Di Guida, May 19 2012

Keywords

Comments

Intersection of A046133 and A033560. - M. F. Hasler, May 19 2012

Links

Programs

  • Mathematica
    Select[Range[50], PrimeQ[#] && PrimeQ[# + 12] && PrimeQ[# + 24] &] (* G. C. Greubel, Jun 20 2017 *)
  • PARI
    forprime(p=1,2999,isprime(p+12)&isprime(p+24)&print1(p",")) \\ M. F. Hasler, May 19 2012

A279765 Primes p such that p+24 and p+48 are also primes.

Original entry on oeis.org

5, 13, 19, 23, 59, 79, 83, 89, 103, 149, 233, 269, 283, 349, 373, 409, 419, 439, 443, 499, 523, 569, 593, 653, 709, 773, 829, 839, 859, 863, 929, 1039, 1069, 1259, 1279, 1399, 1423, 1559, 1699, 1753, 1823, 1949, 1979, 2039, 2063, 2089, 2113, 2309, 2333, 2393
Offset: 1

Views

Author

Gerhard Kirchner, Dec 18 2016

Keywords

Comments

Subsequence of A033560. The triples have the form (p,p+d,p+2d). The current sequence (d=24) continues A023241 (d=6), A185022 (d=12) and A156109 (d=18). The frequencies of such triples and the triple (p, p+3±1, p+6) in A007529 do not differ very much (see table in the link "comparison of triples"). For creating the b-file I used a file of prime differences, divided by 2 (extension of A028334). For filling the table I analyzed primes up to 10^9.
Annotation: The algorithm using a file of primes or prime differences is not difficult but not as easy as using a function like isprime(n). On the other hand, such a function needs computing time which is not negligible for large numbers.

Examples

			First term: 5, 5 + 24 = 29 and 5 + 48 = 53 are all primes.

Links

Crossrefs

Cf. A023241, A033560, A156109, A185022.

Programs

  • Mathematica
    Select[Prime@Range@500, PrimeQ[# + 24] && PrimeQ[# + 48] &] (* Robert G. Wilson v, Dec 18 2016 *)
  • PARI
    is(n) = for(k=0, 2, if(!ispseudoprime(n+24*k), return(0))); 1 \\ Felix Fröhlich, Dec 26 2016

A054983 Composite numbers n such that sigma(n+24) = sigma(n) + 24.

Original entry on oeis.org

80, 95, 119, 299, 527, 962, 1247, 1479, 1739, 2783, 4307, 4958, 5240, 6015, 7878, 8342, 10379, 11639, 16967, 20687, 21439, 29294, 34547, 36917, 49022, 51959, 54707, 59807, 76127, 97319, 153242, 181427, 203318, 203822, 213419, 363302, 423999, 494882, 582902
Offset: 1

Views

Author

Labos Elemer, May 29 2000

Keywords

Comments

See also A015914, A054799, A033560

Examples

			a(1) = 80, sigma(80)+24 = 186+24 = 210 = sigma(80+24) = sigma(104) = 104+52+26+13+8+4+2+1.

Links

Crossrefs

Cf. A015914-A015917, A054799.

Programs

  • Mathematica
    With[{nn=200000},Select[Complement[Range[nn],Prime[Range[ PrimePi[nn]]]], DivisorSigma[1,#+24] == DivisorSigma[1,#]+24&]] (* Harvey P. Dale, Jan 12 2013 *)
Showing 1-10 of 16 results. Next

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