A154485 -id:A154485 - cp's OEIS frontend

A154486 a(n+1)-+a(n)=prime, a(1)=0,a(2)=5.

0, 5, 8, 11, 18, 23, 30, 37, 42, 47, 50, 53, 56, 75, 82, 85, 88, 91, 102, 109, 114, 119, 122, 129, 134, 137, 140, 143, 150, 157, 160, 171, 176, 183, 190, 193, 196, 201, 208, 211, 222, 227, 230, 233, 246, 253, 256, 267, 274, 297, 302, 305, 308, 311, 330, 343, 348

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

Sum and difference of any of two consecutive numbers in current sequence are prime numbers : 8-5=3;8+5=13, 11-8=3;11+8=19, 18-11=7;18+11=29,...

Essentially the same as A154484 and A154485.

a=0;b=5;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b],AppendTo[lst,n];a=b;b=n],{n,b+1,7!}];lst

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

A154487 a(n+1)-+a(n)=prime, a(1)=0,a(2)=7.

Original entry on oeis.org

0, 7, 10, 13, 16, 21, 26, 33, 38, 41, 48, 53, 56, 75, 82, 85, 88, 91, 102, 109, 114, 119, 122, 129, 134, 137, 140, 143, 150, 157, 160, 171, 176, 183, 190, 193, 196, 201, 208, 211, 222, 227, 230, 233, 246, 253, 256, 267, 274, 297, 302, 305, 308, 311, 330, 343

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

Sum and difference of any of two consecutive numbers in current sequence are prime numbers : 10-7=3;10+7=17, 230-227=3;230+227=457, 233-230=3;233+230=463,...

Essentially the same as A090955. - R. J. Mathar, Jan 12 2009

Cf. A154484, A154485, A154486

a=0;b=7;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b],AppendTo[lst,n];a=b;b=n],{n,b+1,7!}];lst

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

A154488 a(n+1)-+a(n)=prime, a(1)=1,a(2)=12.

Original entry on oeis.org

1, 12, 17, 20, 23, 30, 37, 42, 47, 50, 53, 56, 75, 82, 85, 88, 91, 102, 109, 114, 119, 122, 129, 134, 137, 140, 143, 150, 157, 160, 171, 176, 183, 190, 193, 196, 201, 208, 211, 222, 227, 230, 233, 246, 253, 256, 267, 274, 297, 302, 305, 308, 311, 330, 343, 348

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

Sum and difference of any of two consecutive numbers in current sequence are prime numbers : 230-227=3;230+227=457, 233-230=3;233+230=463,...

Cf. A154484, A154485, A154486, A154487

a=1;b=12;lst={a,b};Do[If[PrimeQ[n-b]&&PrimeQ[n+b],AppendTo[lst,n];a=b;b=n],{n,b+1,7!}];lst

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

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, ...

Cf. A154484, A154485, A154486, A154487, A154488

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

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, ... .

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

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, ...

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

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, ...

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

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

41+43+47=171,...

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

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

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

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

nonn

			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,... .

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

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

Corrected and extended by Robert Israel, Nov 29 2023

cp's OEIS Frontend

A154486 a(n+1)-+a(n)=prime, a(1)=0,a(2)=5.

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A154487 a(n+1)-+a(n)=prime, a(1)=0,a(2)=7.

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A154488 a(n+1)-+a(n)=prime, a(1)=1,a(2)=12.

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

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

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

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

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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.

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