A328761 The least integer k >= 0 for which A328578(k) = A257993(A276086(A276086(k))) = n.

1, 0, 2, 4, 10, 20, 28, 82, 116, 148, 208, 418, 838, 1048, 1466, 1858, 2276, 4612, 9028, 11546, 16162, 18478, 23098, 27688, 30028, 90086, 147838, 180178, 240232, 297988, 330328, 390358, 450238, 480478, 1021016, 2039728, 3033028, 3573566, 4594558, 5105098, 6606598, 7147136, 8168152, 8678668, 9699688, 29099062, 48498238, 58198138, 77597516, 96996896, 106696588, 126095968

Offset: 1

Author

Antti Karttunen, Oct 27 2019

Keywords

• nonn

Comments

The sequence seems to be monotonic from the second term onward. If this holds, then this sequence (after the initial 1) gives also the positions of records in A328578. See also the scatterplot of A328578.

Links

• Index entries for sequences related to primorial base

Crossrefs

Column 1 of A328631.

Cf. A257993, A276086, A328578.

Programs

PARI

A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328578(n) = A257993(A276086(A276086(n)));
A328761(n) = for(k=0,oo,if(A328578(k)==n,return(k)));

PARI

A328761list(up_to) = { my(v=vector(up_to), k); for(n=0,oo,k=A328578(n); if(k>#v, return(v)); if(!v[k],v[k] = n; print("Found ",k, " at n=",n)); if(k>=#v,return(v))); };
v328761 = A328761list(52);
A328761(n) = if(2==n,0,v328761[n]);