A300247 Restricted growth sequence transform of A286457(n), filter combining A078898(n) and A246277(n).

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 8, 4, 9, 2, 10, 2, 11, 12, 13, 2, 14, 3, 15, 16, 17, 2, 18, 2, 19, 20, 21, 4, 22, 2, 23, 24, 25, 2, 26, 2, 27, 28, 29, 2, 30, 3, 31, 32, 33, 2, 34, 12, 35, 36, 37, 2, 38, 2, 39, 40, 41, 42, 43, 2, 44, 45, 46, 2, 47, 2, 48, 49, 50, 4, 51, 2, 52, 53, 54, 2, 55, 56, 57, 58, 59, 2, 60, 12, 61, 62, 63, 64, 65, 2, 66

Offset: 1

Author

Antti Karttunen, Mar 03 2018

Keywords

• nonn
• look

Comments

For all i, j:

a(i) = a(j) => A280492(i) = A280492(j).

a(i) = a(j) => A300248(i) = A300248(j).

The latter follows because A046523(n) = A046523(2*A246277(n)).

Examples

			a(65) = a(119) (= 42) because A078898(65) = A078898(119) = 5 (both numbers occur in column 5 of A083221) and because A246277(65) = A246277(119) = 7 (both numbers occur in column 7 of A246278). Note that 65 = 5*13 = prime(3)*prime(6) and 119 = 7*17 = prime(4)*prime(7) = A003961(65). A246277(n) contains complete information about the (relative) differences between prime indices in the prime factorization of n.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A078898, A246277, A286457.

Cf. also A300248, A280492.

Programs

PARI

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; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A020639(n) = { if(1==n,n,vecmin(factor(n)[, 1])); };
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A078898(n) = { if(n<=1,n, my(spf=A020639(n),k=1,m=n/spf); while(m>1,if(A020639(m)>=spf,k++); m--); (k)); }; \\ Antti Karttunen, Mar 03 2018
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
A286457(n) = if(1==n,0,(1/2)*(2 + ((A078898(n)+A246277(n))^2) - A078898(n) - 3*A246277(n)));
write_to_bfile(1,rgs_transform(vector(65537,n,A286457(n))),"b300247.txt");