A036319 Composite numbers whose prime factors have no digits other than 4's and 9's.

201601, 224051, 249001, 2244551, 2494501, 4467101, 4964551, 19957601, 22180051, 22225051, 22449551, 24700001, 24949501, 24990001, 42632101, 42654551, 47379551, 47404501, 49735051, 90518849, 98982601, 100598899, 111801449, 124251499, 199557601, 221780051, 222200551, 247445501

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• easy
• base

Comments

Closed under multiplication. - David A. Corneth, Sep 21 2020

From M. F. Hasler, Sep 22 2020: (Start)

Also closed under LCM, but not under GCD.

All terms are congruent to 1 or 9 (mod 10), depending on the parity of their number of prime factors counted with multiplicity, A001222. (End)

Examples

			The smallest prime made up of 4's and 9's is 449 (see A020466), so the smallest term here is 449^2 = 201601. - _N. J. A. Sloane_, Sep 21 2020
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to prime factors.

Crossrefs

Cf. A001222, A020466, A036302-A036325.

Programs

Mathematica

cn49Q[n_]:=Module[{fi=FactorInteger[n][[All,1]]},CompositeQ[n]&&Union[ Flatten[ IntegerDigits/@fi]]=={4,9}&&AllTrue[fi,PrimeQ]]; Select[Range[ 1,1006*10^5,2],cn49Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2020 *)

PARI

is(N)={!isprime(N)&& !#setminus(Set(concat(apply (digits, factor(N)[,1]))), [4,9])} \\ M. F. Hasler, Sep 22 2020

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020466} (p/(p - 1)) - Sum_{p in A020466} 1/p - 1 = 0.00001523788893... . - Amiram Eldar, May 22 2022

Extensions

More terms from David A. Corneth, Sep 21 2020