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 1-3 of 3 results.

A240749 Numbers n such that prime(n)^2 + prime(n+1)^2 is a semiprime.

Original entry on oeis.org

2, 3, 6, 14, 30, 35, 37, 39, 41, 46, 52, 57, 68, 81, 82, 97, 101, 104, 112, 123, 126, 145, 154, 175, 189, 195, 209, 215, 221, 222, 259, 264, 272, 276, 308, 312, 314, 343, 357, 367, 370, 373, 389, 398, 399, 403, 411, 416, 418, 425, 432, 436, 447, 456, 462, 471, 473, 477, 485, 487, 489, 499, 509, 520, 538, 547
Offset: 1

Views

Author

Zak Seidov, Apr 11 2014

Keywords

Comments

a(n) = position of A216432(n) in A069484.

Examples

			a(1) = 2: prime (2)^2 + prime (3)^2  = 3^2 + 5^2 = 34 = A069484(2) = A216432 (1).
a(2) = 3: prime (3)^2 + prime (4)^2  = 5^2 + 7^2 = 74 = A069484(3)  = A216432 (2).
a(3) = 6: prime (6)^2 + prime (7)^2  = 13^2 + 17^2 = 458 = A069484(6)  = A216432 (3).

Links

Crossrefs

Cf. A069484, A216432.

Programs

  • Maple
    with(numtheory):
isok := n -> evalb(bigomega(ithprime(n)^2 + ithprime(n+1)^2) = 2);
A240749_list := n -> select(isok, [$1..n]); A240749_list(555); # Peter Luschny, Apr 12 2014
  • Mathematica
    Position[Total/@Partition[Prime[Range[600]]^2,2,1],?(PrimeOmega[#] == 2&)]// Flatten (* _Harvey P. Dale, Apr 12 2017 *)
  • PARI
    isok(n) = bigomega(prime(n)^2  + prime(n+1)^2) == 2;
lista(nn) = {for(n=1, nn, if (isok(n), print1(n, ", ")));} \\ Michel Marcus, Apr 12 2014
  • PARI
    s=[]; for(n=2, 600, if(isprime((prime(n)^2+prime(n+1)^2)/2), s=concat(s, n))); s \\ Colin Barker, Apr 12 2014

A242218 Semiprimes which are the arithmetic mean of three consecutive primes.

Original entry on oeis.org

511, 537, 1073, 1461, 1501, 1541, 1763, 2071, 2181, 2449, 4101, 4387, 4399, 4467, 4559, 4607, 4681, 4705, 5089, 5257, 5429, 6415, 6621, 6671, 7097, 7111, 7261, 7391, 7447, 7811, 7831, 7897, 7909, 7969, 8079, 8129, 8193, 8333, 8639, 8915, 9101, 9113, 9123, 9211
Offset: 1

Views

Author

K. D. Bajpai, May 07 2014

Keywords

Examples

			a(1) = 511 = (503 + 509 + 521)/3 = 7 * 73 is semiprime.
a(2) = 537 = (523 + 541 + 547)/3 = 3 * 179 is semiprime.

Links

Crossrefs

Cf. A001358, A133529, A216432, A234297.

Programs

  • Maple
    with(numtheory): A242218:= proc()local k ; k:=(ithprime(x)+ithprime(x+1)+ithprime(x+2))/3; if k=floor(k) and bigomega(k)=2 then RETURN (k);  fi; end: seq(A242218 (),x=2..2000);
  • PARI
    for(k=1, 2000, t=prime(k)+prime(k+1)+prime(k+2); if(t%3==0 && bigomega(t/3)==2, print1(t/3, ", "))) \\ Colin Barker, May 08 2014

A242209 Semiprimes sp = p^2 + q^2 + r^2 where p, q and r are consecutive primes.

Original entry on oeis.org

38, 339, 579, 1731, 5739, 8499, 32259, 133851, 145779, 163851, 207579, 222531, 235779, 260187, 308019, 323619, 366819, 469731, 550491, 644979, 684699, 743091, 926427, 1003539, 1242939, 1743531, 1808259, 1852107, 1909059, 2075091, 2585571, 4226979, 5358291
Offset: 1

Views

Author

K. D. Bajpai, May 07 2014

Keywords

Comments

Subsequence of A133529.
All the terms in the sequence, except a(1), are divisible by 3.

Examples

			a(1) = 38 = 2^2 + 3^2 + 5^2 = 2*19 is semiprime.
a(2) = 339 = 7^2 + 11^2 + 13^2 = 3*113 is semiprime.

Links

Crossrefs

Cf. A001358, A133529, A216432.

Programs

  • Maple
    with(numtheory): A242209:= proc()local k ; k:=(ithprime(x)^2+ithprime(x+1)^2+ithprime(x+2)^2); if bigomega(k)=2 then RETURN (k); fi;end: seq(A242209 (),x=1..500);
  • Mathematica
    Select[Total[#^2]&/@Partition[Prime[Range[300]],3,1],PrimeOmega[#]==2&] (* Harvey P. Dale, Nov 05 2015 *)
  • PARI
    for(k=1, 500, sp=prime(k)^2+prime(k+1)^2+prime(k+2)^2; if(bigomega(sp)==2, print1(sp, ", "))) \\ Colin Barker, May 07 2014
Showing 1-3 of 3 results.

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