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 A255063 Number of times an evil number is encountered when iterating from 2^(n+1)-2 to (2^n)-2 with the map x -> x - (number of runs in binary representation of x). 7
 1, 0, 1, 2, 2, 5, 7, 14, 24, 52, 84, 173, 290, 586, 1038, 2025, 3740, 7177, 13498, 25832, 49027, 93918, 179291, 344128, 660058, 1270590, 2447944, 4728357, 9145214, 17718039, 34365068, 66717630, 129619518, 251953756, 489964171, 953141850, 1854911347 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA a(n) = Sum_{k = A255062(n) .. A255061(n+1)} A254113(k). a(n) = Sum_{k = A255062(n) .. A255061(n+1)} A010059(A255066(k)). Other identities. For all n >= 1: a(n) = A255071(n) - A255064(n). EXAMPLE For n=0 we count the evil numbers (A001969) found in range A255056(0..0), and A255056(0) = 0 is an evil number, thus a(0) = 1. For n=1 we count the evil numbers in range A255056(1..1), and A255056(1) = 2 is not an evil number, thus a(1) = 0. For n=2 we look at the numbers in range A255056(2..3), i.e. 4 and 6 and while 4 is not an evil number, 6 is, thus a(2) = 1. For n=5 we look at the numbers in range A255056(12..20) which are (32, 36, 42, 46, 50, 54, 58, 60, 62). Or we take them in the order they come when iterating A236840 (as in A255066(12..20): 62, 60, 58, 54, 50, 46, 42, 36, 32), that is, we start iterating with map m(n) = A236840(n) from the initial value (2^(5+1))-2 = 62. Thus we get m(62) = 60, m(60) = 58, m(58) = 54, m(54) = 50, m(50) = 46, m(46) = 42, m(42) = 36 and finally m(36) = 32 which is (2^5). Of the nine numbers encountered, only 60, 58, 54, 46 and 36 are evil numbers, thus a(5) = 5. PROG (PARI) \\ Compute sequences A255063, A255064 and A255071 at the same time, starting from n=1: A005811(n) = hammingweight(bitxor(n, n\2)); write_A255063_and_A255064_and_A255071(n) = { my(k, i, s63, s64); k = (2^(n+1))-2; i = 1; s63 = 0; s64 = 0; while(1, if((hammingweight(k)%2), s64++, s63++); k = k - A005811(k); if(!bitand(k+1, k+2), break, i++)); write("b255063.txt", n, " ", s63); write("b255064.txt", n, " ", s64); write("b255071.txt", n, " ", i); }; for(n=1, 36, write_A255063_and_A255064_and_A255071(n)); (Scheme, different versions) (define (A255063 n) (if (zero? n) 1 (let loop ((i (- (expt 2 (+ 1 n)) 4)) (s (modulo (+ 1 n) 2))) (cond ((pow2? (+ 2 i)) s) (else (loop (- i (A005811 i)) (+ s (A010059 i)))))))) (define (pow2? n) (and (> n 0) (zero? (A004198bi n (- n 1))))) ;; Alternatively: (define (A255063 n) (add A254113 (A255062 n) (A255061 (+ 1 n)))) (define (A255063 n) (add (COMPOSE A010059 A255066) (A255062 n) (A255061 (+ 1 n)))) CROSSREFS Cf. A001969, A005811, A010059, A236840, A254113, A255056, A255064, A255066, A255071. Similar sequences: A255125, A218542. Sequence in context: A265813 A259864 A028303 * A195964 A047083 A238422 Adjacent sequences:  A255060 A255061 A255062 * A255064 A255065 A255066 KEYWORD nonn AUTHOR Antti Karttunen, Feb 14 2015 STATUS approved

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Last modified July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)