Geodesic
Adding or removing an element from a pseudo-symmetric numerical semigroup
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 681-696

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If $S$ is a pseudo-symmetric numerical semigroup, $g$ is its Frobenius number and $S$ is a minimal generator of $S$, then $S \cup \{g\}$, $S \setminus \{g\}$S and $S \cup \{\frac{1}{2}g, g\}$ are also numerical semigroups. In this paper we study these constructions. 
@article{BUMI_2006_8_9B_3_a10,
     author = {Rosales, J. C.},
     title = {Adding or removing an element from a pseudo-symmetric numerical semigroup},
     journal = {Bollettino della Unione matematica italiana},
     pages = {681--696},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {3},
     year = {2006},
     zbl = {1147.20052},
     mrnumber = {MR2274120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a10/}
}
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Rosales, J. C. Adding or removing an element from a pseudo-symmetric numerical semigroup. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 681-696. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a10/