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

1,1

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.

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

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

Crossrefs

Cf. A003591, A020459, A036302-A036325.

Sequence in context: A331871 A331965 A331683 * A312338 A312339 A024805

Adjacent sequences: A036309 A036310 A036311 * A036313 A036314 A036315

Keyword

nonn,easy,base

Author

Patrick De Geest, Dec 15 1998

Status

approved