A319689 Number of distinct values of A078898 that occur when map x -> A064989(x) is iterated, starting from x = n, until an even number is reached; a(1) = 0 by convention.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2

Offset

1,21

Comments

Number of distinct values that A078898 obtains when applied to n and all the terms above it in that column where it is located in array A246278.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Prog

(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A078898(n) = v078898[n];
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)};
A319689(n) = if(1==n, 0, my(m=Map(), s, k=0); while(1, if(!mapisdefined(m, s=A078898(n)), mapput(m, s, s); k++); if(!(n%2), return(k)); n = A064989(n)));

Crossrefs

Cf. A064989, A078898.

Cf. also A246278, A319679.

Sequence in context: A364388 A242073 A245477 * A373216 A303824 A106751

Adjacent sequences: A319686 A319687 A319688 * A319690 A319691 A319692

Keyword

nonn

Author

Antti Karttunen, Nov 20 2018

Status

approved