A036312 Composite numbers whose prime factors contain no digits other than 2 and 7.

4, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 128, 196, 224, 256, 343, 392, 448, 454, 512, 554, 686, 784, 896, 908, 1024, 1108, 1372, 1454, 1568, 1589, 1792, 1816, 1939, 2048, 2216, 2401, 2744, 2908, 3136, 3178, 3584, 3632, 3878, 4096, 4432, 4802, 5089, 5488

Offset: 1

Author

Patrick De Geest, Dec 15 1998

Keywords

• nonn
• easy
• base

Comments

All terms are a product of at least two terms of A020459. - David A. Corneth, Oct 09 2020

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5340 terms from Robert Israel)
• Index entries for sequences related to prime factors.

Crossrefs

Cf. A003591, A020459, A036302-A036325.

Programs

Maple

dmax:= 4: # for terms < 2*10^dmax
P:= {2,7}:
L:= {7}:
for d from 1 to dmax-1 do
  L:= map(t -> 2*10^d+t, L) union map(t -> 7*10^d+t, L);
  P:= P union select(isprime,L);
od:
R:= {1}: N:= 2*10^dmax:
for p in P do
  R:= R union map(t -> seq(t*p^j,j=1..floor(log[p](N/t))), R)
od:
sort(convert(R minus P minus {1},list)); # Robert Israel, Aug 04 2020

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020459} (p/(p - 1)) - Sum_{p in A020459} 1/p - 1 = 0.7041098484... . - Amiram Eldar, May 18 2022