A380429 Ulam numbers sandwiched between twin prime numbers.

4, 6, 18, 72, 102, 138, 180, 282, 522, 1020, 1032, 1230, 1428, 2112, 2550, 3390, 3918, 3930, 4260, 4800, 5880, 6552, 6870, 7950, 9240, 12162, 13692, 13758, 14322, 15138, 15642, 15732, 18918, 19698, 21738, 22962, 23028, 23742, 26730, 27282, 30090

Offset

1,1

Comments

All terms are even.

Links

Table of n, a(n) for n=1..41.

Example

4 = 2^2 is a member because is an Ulam number and 3, 5 are a couple of twin primes.
72 = 2^3 * 3^2 is a member because is an Ulam number and 71, 73 are a couple of twin primes.

Maple

N:= 10^5: # for terms <= N
U:= [1, 2]: V:= Vector(N): V[3]:= 1: R:= NULL: count:= 0:
for i from 3 do
   for k from U[-1]+1 to N do
     if V[k] = 1 then
       J:= select(`<=`, U +~ k, N);
       V[J]:= V[J] +~ 1;
       U:= [op(U), k];
       if isprime(k+1) and isprime(k-1) then R:= R, k; count:= count+1;  fi;
       break
     fi
   od;
   if k > N then break fi;
od:
R; # Robert Israel, Jan 24 2025

Mathematica

seq[numUlams_] := Module[{ulams = {1, 2}}, Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[DeleteCases[Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {numUlams}]; Select[ulams, And @@ PrimeQ[# + {-1, 1}] &]]; seq[2500] (* Amiram Eldar, Jan 24 2025, after Jean-François Alcover at A002858 *)

Crossrefs

Intersection of A014574 and A002858.

Cf. A001097.

Sequence in context: A005959 A057393 A196570 * A274992 A317584 A012928

Adjacent sequences: A380426 A380427 A380428 * A380430 A380431 A380432

Keyword

nonn

Author

Massimo Kofler, Jan 24 2025

Status

approved