A068791 -id:A068791 - cp's OEIS frontend

A285885 Ulam numbers n such that 3*n is also an Ulam number.

1, 2, 6, 16, 38, 138, 182, 209, 309, 341, 612, 1030, 1389, 2513, 2584, 2628, 2650, 2750, 3031, 3207, 3290, 3593, 3742, 3874, 3962, 4121, 4155, 4998, 5384, 5797, 6552, 6723, 6833, 7461, 7979, 8453, 8541, 8844, 8949, 9015, 9164, 9577, 10547, 10569, 11197, 11346

Offset: 1

Enrique Navarrete, Apr 27 2017

nonn

It appears that there are many more values in this sequence than in A068791, Ulam numbers n such that 2*n is also an Ulam number.

Robert Israel, Table of n, a(n) for n = 1..1570

Cf. A068791.

N:= 40000: # for terms <= N/3
V:= Vector(N):
U:= [1,2]:
V[3]:= 1:
for i from 3 do
  found:= false;
  for j from U[i-1]+1 to N do
    if V[j]=1 then found:= true; break fi
  od;
  if not found then break fi;
  R:= select(`<=`,j+~U,N):
  V[R]:= 1 +~ V[R];
  U:= [op(U),j];
od:
U:= convert(U,set):
sort(convert(U intersect map(`*`,U,1/3),list)); # Robert Israel, Aug 31 2020

A287612 Ulam numbers k such that 4*k is also an Ulam number.

Original entry on oeis.org

1, 2, 4, 18, 114, 131, 180, 258, 324, 412, 431, 605, 646, 864, 1037, 1081, 1101, 1167, 1296, 1313, 1404, 1470, 1765, 1856, 1858, 1900, 1944, 2032, 2117, 2327, 2572, 2630, 2635, 2674, 2787, 2809, 2814, 2897, 3068, 3214, 3219, 3261, 3393, 3451, 3591, 3622, 3630

Offset: 1

Enrique Navarrete, May 27 2017

nonn

Cf. A002858, A068791, A285885.

(* First run one of the programs for A002858 to populate the ulams list *) A287612 = ulams; curr = 1; While[curr < Length[ulams] + 1, A287612[[curr]] = ulams[[curr]] * Boole[MemberQ[ulams, 4ulams[[curr]]]]; curr++]; DeleteCases[A287612, 0] (* Alonso del Arte, May 28 2017 *)

A068799 Ulam numbers such that n/2 is also an Ulam number.

Original entry on oeis.org

2, 4, 6, 8, 16, 26, 36, 72, 106, 114, 138, 412, 546, 800, 1966, 2616, 5162, 6410, 8236, 27062, 29784, 177104, 278256, 342486, 556126, 664364, 1388708, 6833546, 8622762, 9734048

Offset: 1

Naohiro Nomoto, Mar 29 2002

Cf. A002858, A068791.

a(n) = 2 * A068791(n). - Sean A. Irvine, Mar 15 2024

More terms from Jud McCranie, Feb 12 2003

A287613 Ulam numbers u such that 5*u is also an Ulam number.

Original entry on oeis.org

36, 97, 138, 206, 358, 402, 722, 2816, 3205, 3725, 3918, 3962, 5020, 5516, 7461, 8368, 8756, 9193, 9621, 10247, 11219, 11586, 11759, 12365, 12580, 12602, 13164, 13401, 14892, 15820, 17743, 18305, 19644, 20140, 22344, 24785, 29733, 32626, 33276, 34549, 34615, 35888

Offset: 1

Enrique Navarrete, May 27 2017

nonn

As in the case k=2, these are very scarce Ulam numbers u with the property that k*u is also an Ulam number (see link).

Enrique Navarrete, Relative Frequencies of Multiples of Ulam Numbers

Cf. A002858, A068791, A285885, A287612.

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A285885 Ulam numbers n such that 3*n is also an Ulam number.

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A287612 Ulam numbers k such that 4*k is also an Ulam number.

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A068799 Ulam numbers such that n/2 is also an Ulam number.

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A287613 Ulam numbers u such that 5*u is also an Ulam number.

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