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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 March 30 04:12 EDT 2023. Contains 361603 sequences. (Running on oeis4.)