A154952 Index of first occurrence of n in A154404.

1, 5, 6, 7, 12, 9, 13, 17, 22, 20, 26, 56, 50, 46, 74, 106, 76, 152, 116, 242, 206, 284, 623, 1056, 1032, 1582, 1586, 1616, 1892, 1676, 4286, 5484, 4946, 7016, 5366, 11262, 18776, 17486, 19688, 18192, 21018, 60662, 51476, 56546, 79946, 66986, 105476

Offset: 0

Author

Jon E. Schoenfield, Jan 18 2009

Keywords

• nonn

Comments

A related problem is to determine the index of the last occurrence of n in A154404. Among the first 10^6 terms in A154404, the values 0, 1, 2 and 3 last occur at indices 4, 5, 6 and 8, respectively, but all values larger than 3 that occur at all (4 through 56 and 58 through 61) do so at least once beyond the 500000th term.

The value 4, after its initial occurrence in A154404 at n=12, does not reoccur until n=666393. (The 4 ways to reach 666393 as a sum of an odd prime, a positive Fibonacci number and a Catalan number are 605023+2584+58786, 606997+610+58786, 607573+34+58786 and 648677+17711+5.)

Examples

			a(4) = 12 because 12 is the smallest number that can be expressed in exactly 4 ways as the sum of an odd prime, a positive Fibonacci number and a Catalan number. (The 4 ways are 3+8+1, 5+2+5, 5+5+2 and 7+3+2.)
		

Crossrefs

Cf. A154404