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 1-3 of 3 results.

A181620 Sequence starting with 2 such that the sum of any two distinct terms is a semiprime having two distinct prime factors.

Original entry on oeis.org

2, 4, 31, 91, 183, 4411, 29611, 59935, 110791, 10418851, 658653031, 20123369491, 518294316451, 947137685251
Offset: 1

Views

Author

Michel Lagneau, Jan 31 2011

Keywords

Comments

Choose the first number not leading to a contradiction.
The sequence starting with 1 is finite: {1, 5, 9, 86, 212};
Sequence starting with 3: {3, 7, 19, 32, 55, 246, 39499, ...};
Sequence starting with 4: {4, 6, 29, 89, 137, 749, 1685, 16497, ...}.

Examples

			The subset {2, 4, 31} produces the three sums {6, 33, 35} which factor as {2*3, 3*11, 5*7}.
		

Crossrefs

Programs

  • Maple
    with(numtheory):nn:=500000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
      nn do: T[p]:=p+1:U[p]:=2:od:for u from 1 to 10 do: k:=1+u:for n from u+1 to
      nn do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=2 and s2=2 then
      U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
      1 to 30 do:print( T[j]):od:
  • Mathematica
    TwoDistinct[n_]:=Module[{p,e}, {p,e}=Transpose[FactorInteger[n]]; Length[p]==2 && e=={1,1}]; t={2}; k=2; Do[While[k++; !And@@TwoDistinct/@(k+t)]; AppendTo[t,k], {6}]; t

Extensions

Removed 84835 and a(10)-a(12) from Donovan Johnson, Feb 14 2011
a(13)-a(14) from Jinyuan Wang, May 29 2025

A181622 Sequence starting with 1 such that the sum of any two distinct terms has three distinct prime factors.

Original entry on oeis.org

1, 29, 41, 281, 401, 1089, 1585, 2289, 4629, 27293, 74873, 965813, 2536781, 4479197, 36730306, 150318056, 4527046433
Offset: 1

Views

Author

Michel Lagneau, Jan 31 2011

Keywords

Comments

Choose the first number not leading to a contradiction.

Examples

			Each of the three pairwise sums of the subset {29, 41, 281} is the product of three distinct prime factors: {2*5*7, 2*5*31, 2*7*23}.
		

Crossrefs

Programs

  • Maple
    with(numtheory):nn:=200000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
      nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 20 do: k:=1+u:for n from u+1 to nn
      do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=3 and s2=3 then
      U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
      1 to 30 do:printf(`%d, `, T[j]):od:

Extensions

a(12)-a(17) from Donovan Johnson, Feb 14 2011

A181623 Sequence starting with 1 such that the sum of any two distinct elements has four distinct prime factors.

Original entry on oeis.org

1, 209, 1121, 2989, 11381, 34889, 47701, 62453, 188785, 878185, 1761737, 3931385, 5630905, 7990481, 32892077, 204570037, 253223785, 1353794333, 2877954833
Offset: 1

Views

Author

Michel Lagneau, Jan 31 2011

Keywords

Comments

Choose the first number not leading to a contradiction.

Examples

			Each of the three pairwise sums of the subset {1, 209, 1121} is the product of four distinct prime factors: {2*3*5*7,  2*3*11*17,  2*3*5*137}.
		

Crossrefs

Programs

  • Maple
    with(numtheory):nn:=100000:T:=array(1..nn): U:=array(1..nn): for p from 1 to
      nn do: T[p]:=p:U[p]:=1:od:for u from 1 to 30 do: k:=1+u:for n from u+1 to nn
      do:s:=T[n]+T[u]:s1:=nops(factorset(s)):s2:=bigomega(s):if s1=4 and s2=4 then
      U[k]:=T[n]:k:=k+1:else fi:od:for i from 1 to nn do:T[i]:=U[i]:od:od:for j from
      1 to 30 do:printf(`%d, `, T[j]):od:

Extensions

a(9)-a(19) from Donovan Johnson, Feb 14 2011
Showing 1-3 of 3 results.