SMARANDACHE PROBLEMS

Any of a few hundreds of unsolved problems and conjectures proposed by F. Smarandache, most of them related to sequences and functions, especially to find out what terms of the Smarandache Sequences are primes or perfect powers.

Examples:

a) The only prime number of the smarandache reverse sequence 1, 21, 321, 4321, ..., 121110987654321, ... in the first 2,739 terms [Weisstein], even more, in the first 10,000 [Micha Fleuren] is: 8281807978...121110987654321 [Stephan].

b) There are infinitely many primes in the smarandache concatenated prime sequence 2, 23, 235, 2357, 235711, 23571113, 2357111317, ... . (Not proved yet). Weisstein checked the first 1,624 terms and found the terms 1, 2, 4, 128, 174, 342, 435, 1429 primes.

References:

[1] C. Ashbacher, Collection of Problems on Smarandache Notions, Erhus Univ. Press, 1996.

[2] K. Atanassov, On the 4-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 33-35.

[3] K. Atanassov, On the 16-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 36-38.

[4] K. Atanassov, On the 22-nd, the 23-rd, and the 24-th Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1998), No. 2, 80-82.

[5] K. Atanassov, On the 37-th, and the 38-th Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 83-85.

[6] K. Atanassov, On the 40-th and 41-st Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 4 (1998), No. 3, 101-104.

[7] K. Atanassov, On the 43-rd and 44-th Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 86-88.

[8] K. Atanassov, On the 61-st, 62-nd, and 63-rd Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 4 (1998), No. 4, 175-182.

[9] K. Atanassov, On the 62-nd Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 100-101.

[10] K. Atanassov, On the 97-th, 98-th, and 99-th Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1998), No. 3, 89-93.

[11] K. Atanassov, On the 100-th, 101-st, and 102-nd Smarandache problems, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 94-96.

[12] K. Atanassov, On the 117-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 97-98.

[13] K. Atanassov, On the 118-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 3, 99.

[14] K. Atanassov, On the 125-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 125.

[15] K. Atanassov, On the 126-th Smarandache problem, <Notes on Number Theory and Discrete Mathematics>, Sophia, Bulgaria, Vol. 5 (1999), No. 1, 39-40.

[16] K. Atanassov, On Some of the Smarandache's Problems, American Research Press, 88p., 1999.

[17] C.Dumitrescu, V.Seleacu, Some Notions and Questions in Number THeory, Erhus Univ. Press, 1994.

[18] K. Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus Univ. Press, 1996.

[19] N.J.A.Sloane, On-line Encyclopedia of Integer Sequences, sequences: A048758, A048759, A048760, A048761, A048762, A048763, A048764, A048765, A048766.

[20] F. Smarandache, Only Problems, Not Solutions!, Xiquan Publ. Hse., fourth edition, 1993.

[21] F. Smarandache, Problems avec and sans... Problems, Somipress, 1983.

[22] <Smarandache Notions Journal>, collection of papers on Smarandache problems, 1990-1999; http://www.gallup.unm.edu/~smarandache/s-number.txt, prim-sum.txt

[23] Stephan, R. W., Factors and Primes in Two Smarandache Sequences, <Smarandache Notions Journal>, Vol. 9, No. 1-2, second edition, 1998, 5-11.

[24] Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, CRC Press, 1998.