A071794 a(n) is the smallest integer > 0 that cannot be obtained from the integers {1, ..., n} using each number at most once and the operators +, -, *, /, ^.

2, 4, 11, 34, 178, 926, 9434

Offset: 1

Author

Koksal Karakus (karakusk(AT)hotmail.com), Jun 06 2002

Keywords

• hard
• more
• nonn

Comments

The old entry a(6) = 791 was incorrect since 791 = (2^5 + 3^4) (1+6). - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007. Also 791 = ((3*5)^4-1)/2^6. - Sam Handler (shandler(AT)macalester.edu) and Kurt Bachtold (kbachtold(AT)route24.net), Feb 28 2007.

I believe that a(7) = 9434 (with approximately 98% certainty). - Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007

Using the Java programming language, my brother and I have independently created 2 programs which absolutely solve this problem for a given index via brute force algorithms. Our process is to systematically generate every possible equation in polish notation, solve it, then add its solution (providing that it is a positive integer) to a list of previous solutions. After all solutions have been calculated, the program references the list to find the lowest missing number. - Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007

Examples

			a(3)=11 because using {1,2,3} we can write 1, 2, 3, 3+1=4, 3+2=5, 3*2=6, 3*2+1=7, 2^3=8, 3^2=9, (3^2)+1=10 but we cannot obtain 11 in the same way.
		

References

• B. Torrence, Arithmetic Combinations, Mathematica in Education and Research, Vol. 12, No. 1 (2007), pp. 47-59.

Links

• Index entries for similar sequences

Crossrefs

Cf. A060315.

Programs

Mathematica

The Torrence article gives a description of how one can use Mathematica to investigate the sequence.

Extensions

a(6) corrected by Bruce Torrence (btorrenc(AT)rmc.edu), Feb 14 2007

a(7) from Michael and David Kent (zdz.ruai(AT)gmail.com), Jul 29 2007