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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 16:45 EDT 2019. Contains 322209 sequences. (Running on oeis4.)