A276156 Numbers obtained by reinterpreting base-2 representation of n in primorial base: a(0) = 0, a(2n) = A276154(a(n)), a(2n+1) = 1 + A276154(a(n)).
0, 1, 2, 3, 6, 7, 8, 9, 30, 31, 32, 33, 36, 37, 38, 39, 210, 211, 212, 213, 216, 217, 218, 219, 240, 241, 242, 243, 246, 247, 248, 249, 2310, 2311, 2312, 2313, 2316, 2317, 2318, 2319, 2340, 2341, 2342, 2343, 2346, 2347, 2348, 2349, 2520, 2521, 2522, 2523, 2526, 2527, 2528, 2529, 2550, 2551, 2552, 2553, 2556, 2557, 2558, 2559, 30030, 30031
Offset: 0
Links
Crossrefs
Cf. A000040, A001511, A002110, A007088, A007814, A019565, A049345, A257993, A276084, A276085, A276154, A351073, A328461, A328473, A328474, A328571, A328831, A328836, A341518, A344591.
Complement of A177711.
Fixed points of A328841, positions of zeros in A328828, A328842, and A329032, positions of ones in A328581, A328582, and A381032.
Positions of terms < 2 in A328114.
Cf. also table A328464 (and its rows).
Programs
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Mathematica
nn = 65; b = MixedRadix[Reverse@ Prime@ Range[IntegerLength[nn, 2] - 1]]; Table[FromDigits[IntegerDigits[n, 2], b], {n, 0, 65}] (* Version 10.2, or *) Table[Total[Times @@@ Transpose@ {Map[Times @@ # &, Prime@ Range@ Range[0, Length@ # - 1]], Reverse@ #}] &@ IntegerDigits[n, 2], {n, 0, 65}] (* Michael De Vlieger, Aug 26 2016 *) -
PARI
A276156(n) = { my(s=0, p=1, r=1); while(n, if(n%2, s += r); n>>=1; p = nextprime(1+p); r *= p); (s); }; \\ Antti Karttunen, Feb 03 2022
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Python
from sympy import prime, primorial, primepi, factorint from operator import mul def a002110(n): return 1 if n<1 else primorial(n) def a276085(n): f=factorint(n) return sum([f[i]*a002110(primepi(i) - 1) for i in f]) def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) # after Chai Wah Wu def a(n): return 0 if n==0 else a276085(a019565(n)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 23 2017
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