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 1-9 of 9 results.

A154493 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=1,a(2)=4.

Original entry on oeis.org

1, 4, 15, 28, 39, 50, 81, 350, 459, 512, 675, 944, 987, 1040, 1917, 1936, 2325, 2378, 2421, 2588, 2745, 2812, 3459, 3488, 3495, 3506, 5667, 5804, 6027, 6074, 24765, 24832, 25479, 25552, 27621, 27848, 27951, 27980, 34101, 34720, 34773, 35344
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 4-1=3;4+1=5;4*1=4, 15-4=11;15+4=19;15*4=60, ...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488

Programs

  • Mathematica
    a=1;b=4;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154494 a(n+1) -+ a(n) = prime, a(n+1)*a(n) = average of twin prime pairs, a(1)=1, a(2)=6.

Original entry on oeis.org

1, 6, 17, 84, 247, 300, 341, 720, 767, 834, 913, 960, 989, 1590, 1741, 2772, 2945, 3102, 3451, 3540, 3563, 4020, 4159, 4812, 5431, 5700, 6131, 6192, 6245, 8586, 9373, 10056, 10163, 10314, 10543, 10944, 11033, 11844, 12055, 13566, 14015, 15048, 15155
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 6-1=5; 6+1=7; 6*1=6, 17-6=11; 17+6=23; 17*6=102, ... .

Links

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493.

Programs

  • Maple
    f:= proc(x) local k;
  for k from x+1 by 2 do
    if isprime(k+x) and isprime(k-x) and isprime(k*x-1) and isprime(k*x+1) then return k fi
  od;
end proc:
R:= 1,6: x:= 6:
for count from 3 to 100 do
  x:= f(x);
  R:= R,x
od:
R; # Robert Israel, Nov 29 2023
  • Mathematica
    a=1;b=6;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154495 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=2,a(2)=9.

Original entry on oeis.org

2, 9, 20, 33, 40, 141, 298, 435, 536, 687, 884, 1197, 1244, 1665, 1792, 2235, 2486, 2595, 2602, 3765, 3784, 4095, 4148, 4605, 4868, 5061, 5330, 6159, 6220, 6579, 6662, 7119, 7162, 7341, 8288, 10791, 11438, 11859, 12142, 12825, 13274, 14553, 14734
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 9-2=7;9+2=11;9*2=18, ...

Links

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494

Programs

  • Maple
    A:= 2,9: b:= 9:
for i from 3 to 100 do
  p:= 2:
  do
    p:= nextprime(p);
    k:= b + p;
    if isprime(b*k+1) and isprime(b*k-1) and isprime(k+b) then
       A:= A,k; b:= k; break
fi od od:
A; # Robert Israel, Jan 01 2024
  • Mathematica
    a=2;b=9;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154496 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=3,a(2)=10.

Original entry on oeis.org

3, 10, 27, 74, 3093, 3104, 3417, 3580, 3597, 3614, 5907, 5960, 6651, 6962, 9045, 9098, 10479, 10708, 13299, 13382, 14055, 14438, 15099, 16082, 16101, 16112, 16521, 16982, 17505, 19328, 19605, 20062, 22131, 22840, 23013, 23036, 23265, 23422
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 10-3=7;10+3=13;10*3=30, ...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495

Programs

  • Mathematica
    a=3;b=10;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1],AppendTo[lst,n];a=b;b=n],{n,b+1,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154497 a(n) is the least prime > a(n-1) such that a(n-2) + a(n-1) + a(n) is prime, with a(1)=3, a(2)=11.

Original entry on oeis.org

3, 11, 17, 19, 23, 29, 31, 37, 41, 53, 73, 97, 101, 109, 127, 131, 139, 149, 151, 157, 179, 211, 223, 227, 233, 241, 269, 277, 281, 349, 353, 359, 379, 433, 467, 499, 521, 523, 557, 577, 587, 613, 631, 743, 757, 769, 821, 827, 829, 883, 947, 967, 983, 1013, 1087
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Examples

			3+11+17 = 31, 11+17+19 = 47, 17+19+23 = 59, ...

Links

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391.

Programs

  • Maple
    A[1]:= 3: A[2]:= 11:
for i from 3 to 100 do
  p:= A[i-1];
  do
    p:= nextprime(p);
    if isprime(A[i-2]+A[i-1]+p) then
       A[i]:= p; break
    fi
  od
od:
seq(A[i],i=1..100); # Robert Israel, Jan 17 2023
  • Mathematica
    a=3;b=11;lst={a,b};Do[c=Prime[n];p=a+b+c;If[PrimeQ[p],AppendTo[lst,c];a=b;b=c],{n,5,6!}];lst

Extensions

NAME adapted to offset by R. J. Mathar, Jun 19 2021
Name corrected by Robert Israel, Jan 17 2023

A154498 Sum of any 3 consecutive numbers is prime, a(1)=41,a(2)=43.

Original entry on oeis.org

41, 43, 47, 59, 61, 71, 79, 83, 89, 97, 107, 109, 131, 139, 149, 151, 157, 179, 211, 223, 227, 233, 241, 269, 277, 281, 349, 353, 359, 379, 433, 467, 499, 521, 523, 557, 577, 587, 613, 631, 743, 757, 769, 821, 827, 829, 883, 947, 967, 983, 1013, 1087, 1091
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

41+43+47=171,...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497

Programs

  • Mathematica
    a=41;b=43;lst={a,b};Do[c=Prime[n];p=a+b+c;If[PrimeQ[p],AppendTo[lst,c];a=b;b=c],{n,15,5!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154500 Sum of any 3 consecutive numbers is prime and |a(n+2) - (a(n+1) + a(n))| is prime, a(1)=3, a(2)=5.

Original entry on oeis.org

3, 5, 11, 13, 17, 23, 27, 33, 37, 39, 63, 65, 69, 93, 95, 105, 111, 115, 123, 129, 145, 147, 165, 175, 183, 219, 229, 285, 315, 319, 357, 363, 367, 393, 411, 425, 447, 489, 493, 549, 555, 563, 615, 669, 713, 729, 765, 775, 801, 807, 839, 885, 897, 901, 915, 933, 941, 945, 957, 995, 1005, 1023, 1051
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Examples

			3+5+11=19; 11-(3+5)=3, 5+11+13=29; 13-(5+11)=-3, 11+13+17=41; 17-(11+13)=-7, 13+17+23=53; 23-(13+17)=-7,... .

Links

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498.

Programs

  • Maple
    R:= 3,5: count:= 2:
a:= 3: b:= 5:
for x from b+2 by 2 while count < 100 do
   if isprime(a+b+x) and isprime(abs(x-(a+b))) then
     R:= R, x; a:= b; b:= x; count:= count+1;
   fi
od:
R; # Robert Israel, Nov 29 2023
  • Mathematica
    a=3;b=5;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,5,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021
Corrected and extended by Robert Israel, Nov 29 2023

A154501 Sum of any 3 consecutive numbers is prime and a(n+2)-(a(n+1)+a(n)) is prime, a(1)=3,a(2)=11.

Original entry on oeis.org

3, 11, 17, 31, 41, 59, 97, 113, 127, 139
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

3+11+17=31;17-(3+11)=3,...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498, A154500

Programs

  • Mathematica
    a=3;b=11;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,5,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

A154502 Sum of any 3 consecutive numbers is prime and a(n+2)-(a(n+1)+a(n)) is prime, a(1)=3,a(2)=31.

Original entry on oeis.org

3, 31, 37, 71, 89, 157, 163
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Keywords

Comments

3+31+37=71;37-(3+31)=3,...

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498, A154500, A154501

Programs

  • Mathematica
    a=3;b=31;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,9,9!}];lst

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021
Showing 1-9 of 9 results.

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