Halakhah su Salmi 119:12

If the place to be read was shown to the oleh and he recited the blessing, and then it was realized that it was not the [right] place, but, rather, another place is to be read, regardless if the reading has started or has not started, [the following must be considered:] if the place [in the Torah] that was to be read was also open before him, [during the berachah], even if it is in another column [as long as it was] past the place that was shown to him, he need not recite a second berachah, because his mind was on the place on which he intended the berachah as well as on whatever was opened before him. But, if the place was not open before him, and they must now roll the Seifer Torah [to the proper place], or even if the place was open before him, but it is located before the place that was shown to him; he must recite the berachah: asher bachar banu a second time. But, Barechu [es Hashem hamevorach] should not be said a second time. He must first (before repeating the berachah) say: Baruch sheim kevod malchuso leolam va'ed³⁶“Blessed is His Name, Whose glorious kingdom is forever and ever.” This is said to somewhat atone for the sin of having mentioned His Name in vain at the first berachah. on the first berachah which was recited in vain. If [the error was realized] when he had said only: Baruch atah Hashem. then he should conclude… lamdeinu chukecha.³⁷Resulting in his having said altogether: בָּרוּךְ אַתָּה ה' לַמְּדֵנִי חֻקֶּיךָ, “Blessed are You, Hashem, teach me Your statutes,” (Ps 119:12) which is a complete verse, thereby avoiding a בְּרָכָה לְבֵטָלָה—a berachah recited in vain. If the place to be read precedes the place shown him, but is close enough to it, and so situated to make it possible that three verses can also be read from the place [upon which] he said the berachah and further, [and with the condition that] it is all included in that day's portion, then this should be done in order to avoid a second berachah.