A364962 Odd numbers k such that A005941(k) is either k itself or its descendant in Doudna-tree, A005940.

1, 3, 5, 11, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 127

Offset: 1

Author

Antti Karttunen, Aug 14 2023

Keywords

• nonn
• hard
• more

Comments

Questions: Is 85 the only composite in this sequence? (See also A364565). Are there any more terms after 127, or is the sequence finite?

Examples

			85 = 5*17 is a term, because A005941(85) = 133 = 7*19 = A003961(85), thus 133 is a left hand side child of 85 in the tree depicted in A005940, and therefore 85 is included in this sequence. (See also the last example in A364959).
		

Crossrefs

Cf. A005940, A005941, A029747, A156552, A252464.

Cf. also A364959, A364961.

Programs

PARI

A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After David A. Corneth's program for A156552)
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)};
A252463(n) = if(!(n%2),n/2,A064989(n));
isA364962(n) = if(!(n%2),0,my(k=A005941(n)); while(k>n, k = A252463(k)); (k==n));