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A sequence search method was developed to search regular frequency spacing indelta Scuti stars by visual inspection and algorithmic search. We searched forsequences of quasi-equally spaced frequencies, containing at least four membersper sequence, in 90 delta Scuti stars observed by CoRoT. We found anunexpectedly large number of independent series of regular frequency spacing in77 delta Scuti stars (from 1 to 8 sequences) in the non-asymptotic regime. Weintroduce the sequence search method presenting the sequences and echellediagram of CoRoT 102675756 and the structure of the algorithmic search. Foursequences (echelle ridges) were found in the 5-21 d^{-1} region, where thepairs of the sequences are shifted (between 0.5-0.59 d^{-1}) by twice the valueof the estimated rotational splitting frequency (0.269 d^{-1}). The generalconclusions for the whole sample are also presented in this paper. Thestatistics of the spacings derived by the sequence search method, by FT andthat of the shifts are also compared. In many stars, more than one almostequally valid spacing appeared. The model frequencies of FG Vir and theirrotationally split components were used to reveal a possible explanation thatone spacing is the large separation, while the other is a sum of the largeseparation and the rotational frequency. In CoRoT 102675756, the two spacings(2.249 and 1.977 d^{-1}) agree better with the sum of a possible 1.710 d^{-1}large separation and two or one times, respectively, the value of therotational frequency.

Unexpected series of regular frequency spacing of delta Scuti stars in the non-asymptotic regime -- I. The methodology