A215198 Numbers n such that n and n + 1 are both of the form p*q^5 where p and q are distinct primes.

8991, 9375, 335583, 364256, 488672, 535328, 677727, 690848, 755487, 768608, 864351, 908576, 924128, 955232, 1097631, 1377567, 1424223, 1608416, 1688607, 1875231, 2121632, 2124063, 2168288, 2277152, 2541536, 2575071, 2621727, 2901663, 3190624, 3241376, 3409375

Offset

1,1

Comments

The smaller of adjacent values in A178740. - R. J. Mathar, Aug 08 2012

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

8991 is a member as 8991 = 37*3^5 and 8992 = 281*2^5.

Maple

with(numtheory):for n from 3 to 10^7 do:x:=factorset(n):y:=factorset(n+1):n1:=nops(x):n2:=nops(y):if n1=2 and n2=2 then xx1:=x[1]*x[2]^5 : xx2:=x[2]*x[1]^5:yy1:=y[1]*y[2]^5: yy2:=y[2]*y[1]^5:if (xx1=n or xx2=n) and (yy1=n+1 or yy2=n+1) then printf("%a, ", n):else fi:fi:od:

Mathematica

lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 5}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 5}, AppendTo[lst, n]]], {n, 3, 10^7}]; lst
SequencePosition[Table[If[Sort[FactorInteger[n][[;; , 2]]]=={1, 5}, 1, 0], {n, 341*10^4}], {1, 1}][[;; , 1]] (* Harvey P. Dale, Nov 04 2023 *)

Crossrefs

Cf. A074172, A178740, A215173, A215197.

Sequence in context: A251234 A144126 A263062 * A202531 A106770 A326319

Adjacent sequences: A215195 A215196 A215197 * A215199 A215200 A215201

Keyword

nonn

Author

Michel Lagneau, Aug 05 2012

Status

approved