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 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)). 34
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Numbers that are sums of distinct primorial numbers, A002110. Numbers with no digits larger than one in primorial base, A049345. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8191 FORMULA a(0) = 0, a(2n) = A276154(a(n)), a(2n+1) = 1+A276154(a(n)). Other identities. For all n >= 0: a(n) = A276085(A019565(n)). A049345(a(n)) = A007088(n). A257993(a(n)) = A001511(n). A276084(a(n)) = A007814(n). 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 *) PROG (Scheme, two versions) ;; Almost standalone, requiring only A000040: (define (A276156 n) (let loop ((n n) (s 0) (pr 1) (i 1)) (cond ((zero? n) s) ((even? n) (loop (/ n 2) s (* (A000040 i) pr) (+ 1 i))) (else (loop (/ (- n 1) 2) (+ s pr) (* (A000040 i) pr) (+ 1 i)))))) ;; One using memoization-macro, implementing the given recurrence: (definec (A276156 n) (cond ((zero? n) n) ((even? n) (A276154 (A276156 (/ n 2)))) (else (+ 1 (A276154 (A276156 (/ (- n 1) 2))))))) (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 CROSSREFS Cf. A000040, A001511, A002110, A007088, A007814, A019565, A049345, A257993, A276084, A276085, A276154. Cf. also A059590. Sequence in context: A257262 A293397 A059590 * A144705 A028733 A028789 Adjacent sequences:  A276153 A276154 A276155 * A276157 A276158 A276159 KEYWORD nonn,base AUTHOR Antti Karttunen, Aug 24 2016 STATUS approved

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Last modified April 17 14:32 EDT 2021. Contains 343063 sequences. (Running on oeis4.)