A308191 a(n) = smallest m such that A308190(m) = n, or -1 if no such m exists.

5, 6, 8, 7, 10, 16, 17, 30, 29, 54, 53, 102, 101, 198, 197, 390, 389, 774, 773, 1542, 3080, 3079, 6154, 12304, 24604, 36901, 73798, 147592, 295180, 295517, 591030, 1182056, 1574849, 3149694, 4728211, 6299383, 12598762, 25197520, 25197533, 50395062, 100790120, 100790119, 201580234, 403160464, 806320924, 1232145821, 2464291638

Offset

0,1

Comments

It seems plausible that m exists for all n >= 0.

From Chai Wah Wu, Jun 14 2019: (Start)

All terms are even or prime. If a(n+1) is even, then 2*a(n)-a(n+1) = 4. a(n+1) <= 2*(a(n)-2) and thus m exists for all n >= 0. The proof in the comments of A308193 is applicable for this sequence as well.

If a(n) is prime, then a(n-1) <= a(n) + 1. For the prime terms 7, 17, 29, 53, 101, 197, 389, 773, 3079, 100790119, a(n-1) = a(n) + 1.

(End)

Links

Chai Wah Wu, Table of n, a(n) for n = 0..54

Crossrefs

Cf. A111234, A308190.

Sequence in context: A330863 A111514 A308195 * A111770 A105738 A099149

Adjacent sequences: A308188 A308189 A308190 * A308192 A308193 A308194

Keyword

nonn

Author

N. J. A. Sloane, Jun 14 2019

Extensions

a(24)-a(41) from Chai Wah Wu, Jun 14 2019

a(42)-a(44) from Chai Wah Wu, Jun 15 2019

a(45)-a(46) from Chai Wah Wu, Jun 16 2019

Status

approved