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A322822 Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(2) = -1, f(n) = 0 if n is a Fermi-Dirac prime (A050376) > 2, and f(n) = A300840(n) for all other numbers. 5
1, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 9, 3, 3, 10, 3, 11, 12, 13, 3, 7, 3, 14, 15, 16, 3, 9, 3, 17, 18, 19, 20, 21, 3, 22, 23, 11, 3, 12, 3, 24, 25, 26, 3, 27, 3, 28, 29, 30, 3, 15, 31, 16, 32, 33, 3, 34, 3, 35, 36, 37, 38, 18, 3, 39, 40, 20, 3, 21, 3, 41, 42, 43, 44, 23, 3, 45, 3, 46, 3, 47, 48, 49, 50, 24, 3, 25, 51, 52, 53, 54, 55, 27, 3, 56, 57, 58, 3, 29, 3, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For all i, j: a(i) = a(j) => A322823(i) = A322823(j).
LINKS
PROG
(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
ispow2(n) = (n && !bitand(n, n-1));
A302777(n) = ispow2(isprimepower(n));
A050376list(up_to) = { my(v=vector(up_to), i=0); for(n=1, oo, if(A302777(n), i++; v[i] = n); if(i == up_to, return(v))); };
v050376 = A050376list(up_to);
A050376(n) = v050376[n];
A052330(n) = { my(p=1, i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A300840(n) = A052330(A052331(n)>>1);
A322822aux(n) = if((2==n), -1, if(A302777(n), 0, A300840(n)));
v322822 = rgs_transform(vector(up_to, n, A322822aux(n)));
A322822(n) = v322822[n];
CROSSREFS
Cf. also A322805, A322807.
Sequence in context: A341883 A175239 A176228 * A305232 A322974 A326201
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 29 2018
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)