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 1-4 of 4 results.

A256382 Numbers n such that n-4 and n+4 are semiprimes.

Original entry on oeis.org

10, 18, 29, 30, 42, 53, 61, 73, 78, 81, 89, 90, 91, 115, 119, 125, 137, 138, 162, 165, 173, 181, 198, 205, 209, 210, 213, 217, 222, 258, 263, 291, 295, 299, 305, 323, 325, 330, 331, 390, 399, 407, 411, 441, 449, 450, 462, 477, 485, 489, 493, 497, 501, 515, 523
Offset: 1

Views

Author

Michel Marcus, Mar 27 2015

Keywords

Comments

A117328 is the subsequence of primes.

Links

Crossrefs

Cf. A001358 (semiprimes).
Cf. A117328 (with primes rather than semiprimes).
Cf. A124936 (n-1 and n+1), A105571 (n-2 and n+2).
Cf. A256381 (n-3 and n+3), A256383 (n-5 and n+5).

Programs

  • Magma
    IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [6..750] | IsSemiprime(n+4) and IsSemiprime(n-4) ]; // Vincenzo Librandi, Mar 29 2015
  • Mathematica
    Select[Range[600], PrimeOmega[# + 4] == PrimeOmega[# - 4] == 2 &] (* Vincenzo Librandi, Mar 29 2015 *)
Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,600}],9,1],?(#[[1]]==#[[9]]==1&),{1},Heads->False]]+4 (* _Harvey P. Dale, Mar 29 2015 *)
  • PARI
    lista(nn,m=4) = {for (n=m+1, nn, if (bigomega(n-m)==2 && bigomega(n+m)==2, print1(n, ", ")););}

A115395 Primes p such that p+-6 are semiprimes.

Original entry on oeis.org

71, 127, 139, 149, 211, 241, 293, 397, 401, 409, 421, 479, 487, 491, 499, 521, 523, 617, 661, 673, 691, 701, 743, 761, 773, 787, 797, 809, 907, 911, 967, 1049, 1061, 1151, 1153, 1163, 1171, 1201, 1213, 1249, 1279, 1399, 1409, 1471, 1523, 1571, 1583, 1597
Offset: 1

Views

Author

Zak Seidov, Mar 08 2006

Keywords

Examples

			71-6=65=5*13 (semiprime), 71+6=77=7*11 (semiprime).

Links

Crossrefs

Cf. A063643 Primes p such that p+-2 are semiprimes, A117328 Primes p such that p+-4 are semiprimes.

Programs

  • Mathematica
    A115395 = {}; k = Prime[n]; Do[If[PrimeOmega[k + 6] == 2 && PrimeOmega[k - 6] == 2, AppendTo[A115395, k]], {n, 1000}]; A115395  (* K. D. Bajpai, Jun 24 2014 *)
  • PARI
    lista(nn) = {pr = primes(nn); pp = select(i->((bigomega(i-6) == 2) && (bigomega(i+6) == 2)), pr); print(pp);} \\ Michel Marcus, Oct 09 2013

A243365 Primes p such that both p^2 + 6 and p^2 - 6 are semiprime.

Original entry on oeis.org

101, 157, 173, 229, 233, 239, 347, 349, 353, 421, 439, 479, 521, 577, 619, 661, 719, 751, 761, 829, 881, 1019, 1061, 1117, 1129, 1153, 1277, 1289, 1321, 1447, 1453, 1489, 1523, 1579, 1721, 1733, 1801, 1811, 1823, 1831, 1861, 1871, 1873, 2027, 2099, 2221, 2239
Offset: 1

Views

Author

K. D. Bajpai, Jun 24 2014

Keywords

Examples

			101 is in the sequence because 101 is prime. 101^2 + 6 = 10207 = 59 * 173 which is semiprime. 101^2 - 6 = 10195 = 5 * 2039 which is semiprime.
157 is in the sequence because 157 is prime. 157^2 + 6 = 24655 = 5 * 4931 which is semiprime. 157^2 - 6 = 24643 = 19 * 1297 which is semiprime.

Links

Crossrefs

Cf. A000040 (primes), A001358 (semiprimes).
Cf. A117328 (p+/-4 semiprime), A115395(p+/-6 semiprime), A242244 (p^2+/-2 semiprime).

Programs

  • Maple
    with(numtheory): A243365:= proc()local k; k:=ithprime(n); if bigomega(k^2+6)=2 and bigomega(k^2-6)=2 then RETURN (k); fi; end: seq(A243365 (),n=1..5000);
  • Mathematica
    A243365 = {}; k = Prime[n]; Do[If[PrimeOmega[k^2 + 6] == 2 && PrimeOmega[k^2 - 6] == 2, AppendTo[A243365, k]], {n, 1000}]; A243365
Select[Prime[Range[400]],PrimeOmega[#^2+{6,-6}]=={2,2}&] (* Harvey P. Dale, Jul 08 2014 *)
  • PARI
    s=[]; forprime(p=2, 3000, if(bigomega(p^2+6)==2 && bigomega(p^2-6)==2, s=concat(s, p))); s \\ Colin Barker, Jun 25 2014

A115396 Smallest prime p such that p+-2n are semiprimes.

Original entry on oeis.org

23, 29, 71, 17, 59, 37, 71, 41, 67, 71, 43, 109, 59, 67, 173, 83, 89, 151, 103, 89, 127, 101, 131, 113, 127, 109, 131, 113, 127, 193, 157, 157, 181, 179, 229, 163, 193, 191, 211, 223, 223, 239, 241, 211, 211, 211, 271, 281, 241, 241, 263, 307, 307, 373, 293
Offset: 1

Views

Author

Zak Seidov, Mar 08 2006

Keywords

Comments

Cf. A063643 Primes p such that p+-2 are semiprimes, A117328 Primes p such that p+-4 are semiprimes.

Examples

			a(100)=571 because 571-2*100=371=7*53 (semiprime), 571+2*100=771=3*257 (semiprime).

Crossrefs

Cf. A063643.
Showing 1-4 of 4 results.

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