A215173 Numbers k such that k and k+1 are both of the form p*q^3 where p and q are distinct primes.

135, 296, 375, 1431, 1592, 3992, 4023, 6183, 7624, 8936, 9368, 10071, 10232, 10375, 10984, 13256, 16551, 16712, 19143, 20871, 22328, 22375, 23031, 24488, 28375, 28376, 28647, 33271, 34856, 35127, 40311, 40472, 41336, 43767, 46791, 49624, 50408, 52375, 53271

Offset

1,1

Comments

Intersection of A065036 and A065036 - 1. - Robert Israel, Jun 15 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2048 from Robert Israel)

Example

135 is a member as 135 = 5*3^3 and 136 = 17*2^3.

Maple

with(numtheory):for n from 1 to 55000 do:x:=factorset(n):y:=factorset(n+1):x2:=sqrt(n):y2:=sqrt(n+1):n1:=nops(x):n2:=nops(y):if n1=2 and n2=2 and bigomega(n) = 4 and bigomega(n+1) = 4 and x2<>floor(x2) and y2<>floor(y2) then printf("%a, ", n):else fi:od:
# Alternative:
N:= 10^5: # to get all terms < N
P1:= select(isprime, {2, seq(2*i+1, i=1..floor(N/16))}):
P2:= select(t -> t^3 <= N/2, P1):
B:= {seq(seq(p^3*q, q=select(`<`, P1, floor(N/p^3)) minus {p}), p=P2)}:
B intersect map(`-`, B, 1); # Robert Israel, Jun 15 2014

Mathematica

lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 3}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 3}, AppendTo[lst, n]]], {n, 3, 55000}]; lst

Crossrefs

Cf. A074172, A065036.

Sequence in context: A342189 A176313 A335328 * A225360 A328651 A159201

Adjacent sequences: A215170 A215171 A215172 * A215174 A215175 A215176

Keyword

nonn

Author

Michel Lagneau, Aug 05 2012

Status

approved