Miroslav Kureš
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 2, Pages 8—15
DOI: 10.7546/nntdm.2019.25.2.815
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Authors and affiliations
Miroslav Kureš
Department of Mathematics, Brno University of Technology
Technicka 2, 61669 Brno, Czech Republic
Abstract
Positive integers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor are studied. They are called the straddled numbers and their properties are derived. There are also presented some findings of such numbers and asymptotic expansions are used, too.
Keywords

 Sums of primes
 Sums of prime powers
 Waring–Goldbachtype problems
2010 Mathematics Subject Classification
 11A51
 11P32
References
 Jakimczuk, R. (2014). Sums of Primes. An Asymptotic Expansion, International Journal of Contemporary Mathematical Sciences, 9 (16), 761–765.
 Kumchev, A. (2005). On theWaring–Goldbach problem for seventh powers, Proceedings of the American Mathematical Society, 133 (10), 2927–2937.
 Kures, M. (2018). Puzzle 1: Sum of Powers of Primes. Available online: http://
searchfornumbers.blogspot.com/2018/08/puzzle1sumofpowersofprimes.html. Accessed: April 9, 2019.  Munafo, R. Notable Properties of Specific Numbers. Available online: https://mrob.com/pub/math/numbers17.html. Accessed: April 9, 2019.
 Rivera, C. Puzzle 98. Curio 39. Available online: https://www.primepuzzles.
net/puzzles/puzz_098.htm. Accessed: April 9, 2019.  Salat, T., & Znam, S. (1968). On sums of the prime powers, Acta Fac. Rer. Nat. Univ. Com. Math., 21, 21–24.
 Sloane, N. J. A. A055233. Composite numbers equal to the sum of the primes from their smallest prime factor to their largest prime factor. Online Encyclopedia of Integer Sequences. Available online: https://oeis.org/A055233. Accessed: April 9, 2019.
 Problem 50: Consecutive prime sum. Project Euler.net. Available online: https://projecteuler.net/problem=50. Accessed: April 9, 2019.
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Cite this paper
Kureš, M. (2019). Straddled numbers: numbers equal to the sum of powers of consecutive primes from the least prime factor to the largest prime factor. Notes on Number Theory and Discrete Mathematics, 25(2), 815, doi: 10.7546/nntdm.2019.25.2.815.