A259397 Numbers n with the property that it is possible to write the base 2 expansion of n as concat(a_2,b_2), with a_2>0 and b_2>0 such that, converting a_2 and b_2 to base 10 as a and b, we have phi(a + b) = phi(n), where phi(n) is the Euler totient function of n.

6, 12, 14, 28, 30, 48, 62, 124, 126, 222, 224, 254, 448, 476, 496, 510, 768, 876, 1022, 1792, 1806, 2032, 2034, 2046, 2625, 2850, 2898, 3204, 3246, 3560, 3705, 3850, 4064, 4094, 7722, 7744, 7920, 7980, 7992, 8060, 8094, 8136, 8148, 8150, 8164, 8190, 11880, 13365

Offset

1,1

Comments

It appears that a or b is equal to 1. In particular, if b=1 we have 2625, 3705, 13365, 25545, 57645, ... that are a subset of A001274.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..150

Example

6 in base 2 is 110. If we take 110 = concat(1,10) then 1 and 10 converted to base 10 are 1 and 2. Finally phi(1 + 2) = 2 = phi(6).
12 in base 2 is 1100. If we take 1100 = concat(1,100) then 1 and 100 converted to base 10 are 1 and 4. Finally phi(1 + 4) = 4 = phi(12);
2625 in base 2 is 101001000001. If we take 101001000001 = concat(10100100000,1) then 10100100000 and 1 converted to base 10 are 1312 and 1. Finally phi(1312 + 1) = 1200 = phi(2625); etc.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n;
for n from 1 to q do c:=convert(n, binary, decimal);
for k from 1 to ilog10(c) do
a:=convert(trunc(c/10^k), decimal, binary);
b:=convert((c mod 10^k), decimal, binary);
if a*b>0 then if phi(a+b)=phi(n) then print(n); break;
fi; fi; od; od; end: P(10^8);

Crossrefs

Cf. A000010, A001274, A258813, A258843, A258844.

Sequence in context: A315614 A118586 A293907 * A183029 A113791 A292289

Adjacent sequences: A259394 A259395 A259396 * A259398 A259399 A259400

Keyword

nonn,base

Author

Paolo P. Lava, Jun 26 2015

Status

approved