\version "2.19.25"

#(define ls (list))

#(define (reset-part-first-page layout props arg)
  (let* ((actual-book-page (chain-assoc-get 'page:page-number props -1))
         (actual-part-first-page
           (ly:output-def-lookup layout 'first-page-number 1))
         (reset-part-first-page-number
           (ly:output-def-lookup layout 'reset-part-first-page-number #f))
         (new-props 
           (if reset-part-first-page-number
               (prepend-alist-chain
                 'page:page-number-string 
                 (number->string 
                   ;; In case `reset-part-first-page-number' was set #t, do some
                   ;; calculation to put out every bookpart starting with 
                   ;; page-number 1, increasing the follow page-numbers
                   ;;
                   ;; Otherwise we try to find a list of page-settings, probably
                   ;; stored in `reset-part-first-page-number'.
                   ;; If found, we choose the appropiate entry and do some 
                   ;; calculations to put out this entry as the new
                   ;; bookparts-first-page-number, with incresing follow ups.
                   (if (boolean? reset-part-first-page-number)
                       (- actual-book-page (1- actual-part-first-page))
                       (begin 
                         ;; `ls' is defined in \paper
                         ;; accumulate there every part-first-page, if not 
                         ;; already present. 
                         (if (or (null? ls)
                                 (not (= (car ls) actual-part-first-page)))
                             (set! ls (cons actual-part-first-page ls)))
                         ;; (length ls) shows us how many bookparts are present 
                         ;; at the state of current compilation.
                         ;; Therefore we can use (length ls) to choose which  
                         ;; element of `reset-part-first-page-number' should be 
                         ;; taken for the new book-part-first-page-number.
                         ;; list-ref starts with 0, therefore we do 1-
                         ;; As a fall-back, put out the real `actual-book-page'
                         (if (or (< (length reset-part-first-page-number) 
                                    (length ls))
                                 (null? ls))
                             actual-book-page
                             (let ((bookpart-new-first-page
                                     (list-ref 
                                       reset-part-first-page-number 
                                       (1- (length ls)))))
                              ;; Put out `actual-book-page', if a boolean was
                              ;; catched from `reset-part-first-page-number'
                              (if (boolean? bookpart-new-first-page)
                                  actual-book-page
                                  (+ (- actual-book-page actual-part-first-page)
                                     bookpart-new-first-page)))))))
                 props)
               props)))
    (interpret-markup layout new-props arg)))

\paper {
  %% This list may contain booleans, to get default page-counting for a certain
  %% bookpart
  reset-part-first-page-number = #'(1 60 17 613 41)
  oddHeaderMarkup = \markup
  \fill-line {
    " "
    \on-the-fly #print-page-number-check-first
      \on-the-fly #reset-part-first-page
      \fromproperty #'page:page-number-string
  }
  
  evenHeaderMarkup = \markup
  \fill-line {
    \on-the-fly #print-page-number-check-first
      \on-the-fly #reset-part-first-page
      \fromproperty #'page:page-number-string
    " "
  }
}

%%%%%%%%%%%%%%%%%%
%% EXAMPLE
%%%%%%%%%%%%%%%%%%

#(set-default-paper-size "a6")

\book {
  \markuplist \table-of-contents
  \pageBreak
  \markup "Prolog"
  
  \bookpart {
    \markup "first bookpart"
    \tocItem "first bookpart"
    \repeat unfold 3 { c''1 \pageBreak }
  }
  \bookpart {
    \markup "second bookpart"
    \tocItem "second bookpart"
    \repeat unfold 2 { d''1 \pageBreak }
  }
  \bookpart {
    \markup "third bookpart"
    \tocItem "third bookpart"
    \repeat unfold 4 { e''1 \pageBreak }
  }
  \bookpart {
    \markup "fourth bookpart"
    \tocItem "fourth bookpart"
    \repeat unfold 5 { f''1 \pageBreak }
  }
}