A138756 Indices of record values in A138753 (a "prime" variation of the Collatz (3n+1) problem).

1, 2, 3, 8, 11, 17, 18, 27, 42, 72, 125, 219, 221, 401, 515, 556, 754, 841, 1146

Offset: 1

Author

M. F. Hasler, Apr 01 2008

Keywords

• nonn
• hard
• more

Comments

"Indices of ..." is equivalent to "starting values for ..."

Crossrefs

Cf. A124123, A138750-A138754, A171938, A006877 (analog for Collatz problem).

Programs

Mathematica

A138754[n_]:=A138754[n]=With[{p=Prime[n]},PrimePi[NextPrime[If[Mod[p,3]==2,p/2,2p]]]];
A138753[n_]:=Length[NestWhileList[A138754,n,UnsameQ,{1,4}]]-1;
A138756list[upto_]:=Module[{v,r=0},Table[If[(v=A138753[n])>r,r=v;n,Nothing],{n,upto}]];
A138756list[500] (* Paolo Xausa, Jul 30 2023 *)

PARI

m=0; for( i=1,#A138753, A138753[i] > m || next; m=A138753[i]; print1(i", "))

Formula

a(n) = min { k | A138753(k) = A171938(n) }

Equals { m | A138753(k) < A138753(m) for all k

Extensions

a(15)-a(19) from Paolo Xausa, Jul 30 2023

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