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 1-8 of 8 results.

A212881 Numbers k such that k^3 - prime(k) is prime.

Original entry on oeis.org

2, 10, 38, 42, 44, 50, 66, 74, 80, 90, 160, 178, 186, 190, 220, 224, 228, 234, 238, 240, 242, 256, 260, 270, 272, 280, 298, 342, 366, 368, 376, 380, 396, 400, 430, 462, 474, 476, 486, 504, 518, 526, 590, 596, 598, 610, 628, 668, 670, 672, 696, 700, 702, 714
Offset: 1

Views

Author

Zak Seidov, May 29 2012

Keywords

Comments

All terms are trivially even.

Links

Crossrefs

Cf. A064712, A212883.

Programs

  • Magma
    [n: n in [1..400]|IsPrime(n^3-NthPrime(n))];
  • Mathematica
    Reap[Do[If[PrimeQ[n^3-Prime[n]],Sow[n]],{n,2,1000,2}]][[2,1]]
Select[2*Range[400],PrimeQ[#^3-Prime[#]]&] (* Harvey P. Dale, Apr 28 2022 *)

A188831 Primes of the form k^2 - prime(k).

Original entry on oeis.org

23, 71, 107, 263, 487, 677, 787, 1427, 1583, 2081, 3319, 5393, 8713, 10247, 11071, 12377, 18257, 20477, 24659, 26573, 29243, 29927, 33487, 34949, 37223, 37991, 41981, 51449, 60917, 64937, 66977, 71167, 83357, 85667, 99013, 100271, 109313, 110629, 118757
Offset: 1

Views

Author

Zak Seidov, Apr 11 2011

Keywords

Comments

Or, primes in A073497. Corresponding values of k in A064712.
This is to A073497 and A064712 as A184935 is to A004232 and A064711.
The two primes prime(k) and k^2-prime(k) are a Goldbach partition of k^2. - T. D. Noe, Apr 14 2011

Examples

			23 is here because 6^2 - prime(6) = 36 - 13 = 23.

Links

Crossrefs

Cf. A004232, A064711, A064712, A073497, A184935.

Programs

  • Magma
    [ a: k in [0..10000] | IsPrime(a) where a is k^2-NthPrime(k) ]; // Vincenzo Librandi, Apr 14 2011
  • Mathematica
    Select[Table[k^2 - Prime[k], {k, 1000}], PrimeQ] (* T. D. Noe, Apr 14 2011 *)

Formula

a(n) = A073497(A064712(n)).

A212883 Numbers n such that n^4 - prime(n) is prime.

Original entry on oeis.org

2, 6, 40, 76, 144, 146, 148, 166, 168, 174, 186, 192, 210, 220, 222, 230, 238, 240, 258, 290, 338, 364, 372, 378, 384, 398, 400, 402, 442, 446, 482, 492, 532, 536, 554, 570, 606, 628, 654, 700, 740, 882, 888, 944, 954, 964, 966, 978, 1038, 1040, 1072, 1080
Offset: 1

Views

Author

Zak Seidov, May 29 2012

Keywords

Comments

See A064712 for the sequence of values of n such that n^2-prime(n) is prime. - John W. Layman, May 29 2012
All terms are even. - M. F. Hasler, Jun 02 2012

Links

Crossrefs

Cf. A064712, A212881.

Programs

  • Magma
    [n: n in [1..1200]|IsPrime(n^4-NthPrime(n))];
  • Maple
    A[1]:= 2: p:= 3: count:= 1:
for n from 4 to 10^4 by 2 do
   p:= nextprime(nextprime(p));
   if isprime(n^4-p) then
     count:= count+1;
     A[count]:= n;
   fi
od:
seq(A[i],i=1..count); # Robert Israel, Jun 20 2017
  • Mathematica
    Reap[Do[If[PrimeQ[n^4-Prime[n]],Sow[n]],{n,2,1200,2}]][[2,1]]
Select[Range[1200],PrimeQ[#^4-Prime[#]]&] (* Harvey P. Dale, Mar 26 2025 *)
  • PARI
    for(n=1,999,isprime(n^4-prime(n))&print1(n","))  \\ M. F. Hasler, Jun 02 2012

A213428 Numbers k such that k^8 - prime(k) is prime.

Original entry on oeis.org

6, 10, 12, 60, 72, 168, 174, 190, 204, 230, 290, 300, 396, 536, 628, 948, 972, 990, 1014, 1042, 1050, 1174, 1254, 1324, 1326, 1428, 1566, 1602, 1662, 1684, 1808, 1854, 1866, 1942, 1950, 2070, 2154, 2170, 2206, 2214, 2234, 2332, 2388, 2508, 2660, 2668, 2784
Offset: 1

Views

Author

Jonathan Vos Post, Jun 11 2012

Keywords

Comments

k such that A001016(k) - A000040(k) is in A000040.

Examples

			a(1) = 6 because 6^8 - prime(6) = 1679603 is prime.

Links

Crossrefs

Cf. A001016, A064712, A212881, A212883.

Programs

  • Maple
    P:= select(isprime,[2,seq(i,i=3..10^5,2)]):
select(t -> isprime(t^8 - P[t]), [seq(i,i=2..nops(P),2)]); # Robert Israel, Jun 02 2023
  • Mathematica
    Select[Range[3000], PrimeQ[#^8 - Prime[#]] &] (* T. D. Noe, Jun 11 2012 *)

A064483 Numbers k such that k^2 + prime(k) and k^2 - prime(k) are both primes.

Original entry on oeis.org

12, 30, 60, 96, 336, 660, 702, 756, 984, 990, 1188, 1302, 1488, 1830, 1866, 2070, 2142, 2340, 2586, 2874, 2910, 3618, 3714, 3750, 3774, 3906, 4008, 4470, 4512, 4902, 5094, 5754, 6012, 6174, 6432, 6840, 6846, 6930, 7446, 7578, 7734, 8064, 8190, 8328
Offset: 1

Views

Author

Robert G. Wilson v and Jason Earls, Oct 05 2001

Keywords

Comments

All terms are multiples of 6. - Jon E. Schoenfield, Apr 13 2024

Examples

			12 is in the sequence because 144 +/- 37 = 181 and 107 which are both primes.
k=30 is a term: 30^2 = 900, prime(30) = 113, 900+113 = 1013 and 900-113 = 787, both primes.

Links

Crossrefs

Intersection of A064711 and A064712. - Zak Seidov, Oct 12 2014

Programs

  • Mathematica
    Select[ Range[10^4], PrimeQ[ #^2 + Prime[ # ]] && PrimeQ[ #^2 - Prime[ # ]] &]
  • PARI
    for(n=1,20000, if(isprime(n^2+prime(n)) && isprime(n^2-prime(n)), print1(n," ")))
  • PARI
    { n=0; default(primelimit, 6100000); for (m=1, 10^9, if (isprime(m^2 + prime(m)) && isprime(m^2 - prime(m)), write("b064483.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 16 2009

A228828 Numbers n such that n^2 + pi(n) is prime.

Original entry on oeis.org

2, 3, 7, 12, 18, 21, 36, 37, 42, 45, 52, 55, 60, 61, 65, 68, 70, 79, 84, 95, 98, 113, 130, 135, 143, 145, 155, 180, 181, 185, 195, 205, 216, 222, 231, 239, 253, 262, 273, 275, 325, 332, 334, 354, 368, 370, 385, 402, 417, 421, 432, 433, 454, 462, 488, 505, 516
Offset: 1

Views

Author

K. D. Bajpai, Sep 04 2013

Keywords

Comments

Conjecture: the sequence is infinite.

Examples

			a(6) = 21 :  n^2+pi(n ) = 21^2 + pi(21) = 441+8 = 449 which is a prime.

Links

Crossrefs

Cf. A064711, A064712.
Cf. A077510 (numbers n such that n + pi(n) is a prime).

Programs

  • Maple
    with(numtheory): KD:= proc() local a;  a:= n^2+pi(n); if isprime(a) then RETURN(n): fi; end: seq(KD(), n=1..2000);
  • Mathematica
    Select[Range[600],PrimeQ[#^2+PrimePi[#]]&] (* Harvey P. Dale, Jul 04 2018 *)
  • PARI
    v=List(); p=0; for(n=2,1e4,p+=isprime(n); if(isprime(n^2+p), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Sep 04 2013

A213477 Main diagonal starting k=2 of array A(k,n) = numbers n such that n^k - prime(n) is a prime.

Original entry on oeis.org

6, 10, 40, 14, 62, 76, 174, 278, 218, 702, 762, 758, 950, 858, 1782, 2290, 1596, 1462, 1848, 2964, 2262, 4278, 3750, 4320, 5076, 4010, 4890, 8040, 7494, 5962, 7996, 10318, 9424, 5770, 10080, 11088, 12222, 13806, 14712, 16904, 15222, 15620, 18258, 16092
Offset: 1

Views

Author

Jonathan Vos Post, Jun 12 2012

Keywords

Examples

			The array begins:
=====================================================
....|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|
=====================================================
k=2.|...6.|..10.|..12.|..18.|..24.|..28.|..30.|..40.|A064712
k=3.|...2.|..10.|..38.|..42.|..44.|..50.|..66.|..74.|A212881
k=4.|...2.|...6.|..40.|..76.|.144.|.146.|.148.|.166.|A212883
=====================================================

References

  • The k=2 row is A064712 Numbers n such that n^2 - prime(n) is prime.
  • The k=3 row is A212881 Numbers n such that n^3 - prime(n) is prime.
  • The k=4 row is A212883 Numbers n such that n^4 - prime(n) is prime.
  • The k=8 row is A213428 Numbers n such that n^8 - prime(n) is prime.

Crossrefs

Cf. A064712, A212881, A212883.

Programs

  • Mathematica
    Table[Select[Range[100000], PrimeQ[#^n - Prime[#]] &, n-1][[n-1]], {n, 2, 50}] (* T. D. Noe, Jun 13 2012 *)

A213535 Numbers n such that n^5 - prime(n) is prime.

Original entry on oeis.org

2, 8, 10, 14, 30, 40, 50, 190, 294, 308, 346, 370, 396, 400, 630, 634, 690, 716, 746, 790, 870, 912, 926, 968, 1010, 1104, 1122, 1130, 1198, 1204, 1308, 1392, 1394, 1482, 1532, 1560, 1600, 1640, 1706, 1714, 1740, 1742, 1770, 1784, 1810, 1816, 1848, 1880
Offset: 1

Views

Author

Jonathan Vos Post, Jun 13 2012

Keywords

Examples

			a(1) = 2 because 2^5 - prime(2) = 29  a prime.
a(2) = 8 because 8^5 - prime(8) = 32749 is prime.
a(3) = 10 because 10^5 - prime(10) = 99971 is prime.
a(8) = 190 because 190^5 - prime(190) = 247609898849  is prime.

Crossrefs

Cf. A064712, A212881, A212883.

Programs

  • Mathematica
    Select[Range[2000], PrimeQ[#^5 - Prime[#]] &] (* T. D. Noe, Jun 13 2012 *)
Showing 1-8 of 8 results.

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