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 1-10 of 14 results. Next

A072539 Duplicate of A062391.

Original entry on oeis.org

3, 5, 11, 13, 17, 23, 31, 43, 53, 61, 67, 71, 73, 79, 89, 101, 103, 107, 127, 139, 167
Offset: 0

Views

Author

Keywords

A240724 Primes arising in A062391.

Original entry on oeis.org

19, 29, 41, 53, 71, 97, 127, 157, 181, 199, 211, 223, 241, 269, 293, 311, 337, 373, 433, 479, 521, 547, 571, 601, 631, 661, 683, 701, 743, 787, 827, 907, 983, 1061, 1091, 1171, 1279, 1399, 1487, 1543, 1601, 1657, 1721, 1777, 1831, 1987, 2131, 2269, 2347, 2417, 2477, 2539, 2659, 2797, 2897, 2963, 3083
Offset: 1

Views

Author

Zak Seidov, Apr 11 2014

Keywords

Crossrefs

Cf. A062391.

Formula

a(n) = A062391(n) + A062391(n+1) + A062391(n+2).

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

A072537 a(1) = 2, a(2) = 3 and a(n) = the smallest prime which is a linear combination of all previous terms with all coefficients >= 1.

Original entry on oeis.org

2, 3, 5, 13, 23, 53, 101, 211, 419, 839, 1669, 3343, 6689, 13381, 26759, 53527, 107053, 214129, 428221, 856459, 1712899, 3425803, 6851617, 13703231, 27406471, 54812957, 109625881, 219251761, 438503537, 877007063, 1754014121
Offset: 1

Views

Author

Amarnath Murthy, Aug 03 2002

Keywords

Links

Crossrefs

Cf. A072536, A000040, A062391, A151800.

Programs

  • Maple
    A[1]:= 2: A[2]:= 3: S:= 5:
for i from 3 to 50 do
  if S::even then A[i]:= nextprime(S+1)
else A[i]:= nextprime(S-1)
  fi;
S:= S + A[i]
od:
seq(A[i],i=1..50); # Robert Israel, May 01 2019

Formula

For n >= 3, a(n) = A151800(S+(-1)^S) where S = Sum_{i=1..n-1} a(i). - Robert Israel, May 01 2019

Extensions

Corrected and extended by Sascha Kurz, Feb 12 2003

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

A072536 a(1) = 2, a(2) = 3, a(3) = 5 and a(n) = the smallest prime which is a linear combination of previous three terms with all coefficients >=1.

Original entry on oeis.org

2, 3, 5, 13, 29, 47, 89, 223, 359, 983, 2011, 4789, 9749, 24593, 63247, 151429, 414949, 932483, 2368097, 7240291, 17142031, 31486613, 99310681, 245196613, 627886811, 1714144123, 5036961509, 13657860553, 39103788247, 95188254433
Offset: 1

Views

Author

Amarnath Murthy, Aug 03 2002

Keywords

Crossrefs

Cf. A072537, A000040, A062391.

Extensions

More terms from Sascha Kurz, Feb 12 2003

A153075 Increasing sequence of prime numbers such that the sum of any 3 consecutive terms is a prime and sum of any 5 consecutive terms is a prime also.

Original entry on oeis.org

3, 5, 11, 13, 29, 31, 43, 83, 97, 113, 127, 149, 157, 173, 191, 193, 223, 311, 373, 467, 487, 499, 557, 607, 647, 653, 673, 677, 739, 787, 821, 829, 881, 883, 977, 991, 1051, 1217, 1291, 1373, 1427, 1429, 1471, 1583, 1597, 1607, 1609, 1693, 1811, 1877, 1951
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 17 2008, corrected Dec 19 2008

Keywords

Links

Crossrefs

Cf. A153065, A062391.

Programs

  • Maple
    A:= 3,5,11,13:
for n from 1 to 100 do
  s:= A[-1]+A[-2];
  t:= s + A[-3]+A[-4];
  for x from A[-1]+2 by 2 while not(isprime(x)) or not(isprime(x+s)) or not(isprime(x+t)) do od:
  A:= A, x;
od:
A; # Robert Israel, Mar 09 2017
  • Mathematica
    a=3; b=5; c=11; d=13; lst={a, b, c, d}; Do[z=a+b+c+d+n; y=c+d+n; If[PrimeQ[z]&&n>b&&PrimeQ[n]&&PrimeQ[y], AppendTo[lst, n]; a=b; b=c; c=d; d=n], {n, 0, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *)

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

A168322 a(1)=3,a(2)=5; a(n+1)=smallest prime number > a(n-1) such that the sum of any three consecutive terms is a prime.

Original entry on oeis.org

3, 5, 5, 7, 7, 17, 13, 23, 17, 31, 19, 47, 23, 61, 29, 67, 31, 83, 37, 103, 41, 107, 43, 113, 67, 127, 83, 137, 97, 139, 101, 149, 103, 157, 107, 167, 109, 173, 127, 179, 137, 193, 149, 199, 151, 227, 163, 229, 179, 233, 181, 239, 193, 241, 197, 263, 199, 271, 239
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

Keywords

Crossrefs

Cf. A062391

Programs

  • Mathematica
    a=3;b=5;lst={a,b};Do[Do[If[PrimeQ[q]&&PrimeQ[a+b+q],c=q;Break[]],{q,a+2,9!,2}];AppendTo[lst,c];a=b;b=c,{n,6!}];lst
Showing 1-10 of 14 results. Next

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