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.

A213789 A213784/12.

Original entry on oeis.org

1, 7, 17, 38, 95, 452, 837, 917, 1138, 1495, 2317, 3048, 3608, 5232, 6002, 7298, 7315, 7843, 8278, 8932, 10017, 10955, 13458, 13793, 14053, 14970, 15593, 15872, 16485, 17777, 18308, 19590, 19635, 20367, 20983, 21963, 22572, 23793, 24287, 24875, 26225, 26558
Offset: 1

Views

Author

Zak Seidov, Jun 20 2012

Keywords

Formula

a(n) = A213784(n)/12.

A214785 Numbers k such that k + 6 = A214783(k).

Original entry on oeis.org

7, 13, 17, 53, 67, 97, 137, 157, 167, 193, 227, 257, 293, 313, 317, 383, 397, 457, 463, 503, 547, 577, 587, 593, 643, 653, 673, 683, 727, 757, 773, 823, 827, 883, 887, 937, 997, 1013, 1063, 1093, 1163, 1213, 1237
Offset: 1

Views

Author

Art DuPre, Aug 03 2012

Keywords

Comments

This set is disjoint from A213784. Conjecture: all terms are prime.

Crossrefs

Programs

  • Maple
    f:= proc(n) local a,b,t,T,k;
      b:= 0; a:= 1; T:= -3 mod n;
      for k from 1 do
        t:= a+b mod n;
        if t = T then return k+1 fi;
        a:= b; b:= t;
      od
    end proc:
    f(1):= 1: f(3):= 1:
    select(n -> f(n) = n+6, [$1..2000]); # Robert Israel, Jun 08 2023

A213811 Numbers k such that k and k^3 are sums of two twin primes.

Original entry on oeis.org

1044, 1200, 2604, 2964, 4056, 4284, 4476, 7164, 7644, 9300, 9864, 10884, 14616, 15180, 20916, 24084, 40716, 51156, 55056, 65436, 66144, 70104, 74676, 92100, 99060, 104580, 105804, 163944, 164700, 165780, 209604, 218400, 219660, 222540, 226656, 257040, 281676
Offset: 1

Views

Author

Zak Seidov, Jun 20 2012

Keywords

Comments

All terms are multiples of 12.

Examples

			1044=521+523, 1044^3=1137893184=568946591+568946593.
		

Crossrefs

Programs

  • Mathematica
    sttpQ[n_]:=Module[{x=(n-2)/2},AllTrue[{x,x+2},PrimeQ]]; Select[Range[ 12,300000,12],sttpQ[#]&&sttpQ[#^3]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 25 2017 *)
  • PARI
    isok(n) = !(n % 2) && isprime(n/2-1) && isprime(n/2+1) && isprime(n^3/2-1) && isprime(n^3/2+1); \\ Michel Marcus, Oct 19 2013

Formula

k/2 +/-1 and also (k^3)/2 +/- 1 are twin primes.

A212430 Numbers n such that n and n^4 are sums of two twin primes.

Original entry on oeis.org

384, 840, 8676, 33300, 34980, 37044, 39984, 42024, 50604, 53760, 55056, 61680, 64380, 71064, 83520, 88176, 97644, 103740, 120204, 129840, 133896, 148764, 154524, 160416, 168120, 173064, 184800, 188880, 199056, 207984, 234744, 266640, 292116, 307044, 356184
Offset: 1

Views

Author

Zak Seidov, Jun 21 2012

Keywords

Comments

All terms are multiples of 12.

Examples

			384=191+193, 384^3=147456=73727+73729.
		

Crossrefs

Programs

  • Mathematica
    Select[12 Range[30000],AllTrue[{#/2+1,#/2-1,#^4/2+1,#^4/2-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 01 2017 *)
  • PARI
    isok(n) = !(n % 2) && isprime(n/2-1) && isprime(n/2+1) && isprime(n^4/2-1) && isprime(n^4/2+1); \\ Michel Marcus, Oct 19 2013

Formula

n/2 +/-1 and (n^4)/2 +/- 1 are primes.
Showing 1-4 of 4 results.