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 A286240 Compound filter: a(n) = P(A278222(n), A278222(1+n)), where P(n,k) is sequence A000027 used as a pairing function. 5
 2, 5, 12, 14, 23, 42, 59, 44, 23, 61, 142, 117, 109, 183, 261, 152, 23, 61, 142, 148, 601, 850, 607, 375, 109, 265, 1093, 939, 473, 765, 1097, 560, 23, 61, 142, 148, 601, 850, 607, 430, 601, 1741, 3946, 2545, 2497, 3463, 2509, 1323, 109, 265, 1093, 1117, 2497, 4525, 5707, 3153, 473, 1105, 4489, 3813, 1969, 3129, 4497, 2144, 23, 61, 142, 148, 601, 850, 607, 430, 601, 1741 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Antti Karttunen, Table of n, a(n) for n = 0..16383 Eric Weisstein's World of Mathematics, Pairing Function FORMULA a(n) = (1/2)*(2 + ((A278222(n)+A278222(1+n))^2) - A278222(n) - 3*A278222(1+n)). PROG (PARI) A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011 A278222(n) = A046523(A005940(1+n)); A286240(n) = (2 + ((A278222(n)+A278222(1+n))^2) - A278222(n) - 3*A278222(1+n))/2; for(n=0, 16383, write("b286240.txt", n, " ", A286240(n))); (Scheme) (define (A286240 n) (* (/ 1 2) (+ (expt (+ (A278222 n) (A278222 (+ 1 n))) 2) (- (A278222 n)) (- (* 3 (A278222 (+ 1 n)))) 2))) (Python) from sympy import prime, factorint import math def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2 def A(n): return n - 2**int(math.floor(math.log(n, 2))) def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n)) def a005940(n): return b(n - 1) def P(n):     f = factorint(n)     return sorted([f[i] for i in f]) def a046523(n):     x=1     while True:         if P(n) == P(x): return x         else: x+=1 def a278222(n): return a046523(a005940(n + 1)) def a(n): return T(a278222(n), a278222(n + 1)) # Indranil Ghosh, May 07 2017 CROSSREFS Cf. A000027, A278222, A286241, A286242, A286255. Cf. A088705 (one of the matches not matched by A278222 alone. Thus also the whole A007814 (A001511) family is included). Sequence in context: A286255 A286160 A286163 * A215974 A192524 A287553 Adjacent sequences:  A286237 A286238 A286239 * A286241 A286242 A286243 KEYWORD nonn AUTHOR Antti Karttunen, May 07 2017 STATUS approved

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Last modified July 29 06:36 EDT 2021. Contains 346340 sequences. (Running on oeis4.)